Certificate-based encryption and public key infrastructure

ABSTRACT

A digital message is sent from a sender to a recipient in a public-key based cryptosystem comprising an authorizer. The authorizer can be a single entity or comprise a hierarchical or distributed entity. In some embodiments, no key status queries or key escrow are needed. The recipient can decrypt the message only if the recipient possesses up-to-date authority from the authorizer. Other features are also provided.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/521,741, filed Jan. 18, 2005, incorporated herein by reference (nowU.S. Pat. No. 7,657,748, issued on Feb. 2, 2010), which is the U.S.national stage of PCT application PCT/US03/26834, filed Aug. 28, 2003,incorporated herein by reference, which claims the benefit of U.S.provisional patent applications Ser. No. 60/406,721, filed Aug. 28,2002, and 60/412,221, filed Sep. 20, 2002, both which are incorporatedherein by reference.

BACKGROUND OF THE INVENTION

The present invention relates in general to cryptography and securecommunication via computer networks or via other types of systems anddevices, and more particularly to an improved method of implementationof public-key cryptography.

A user of a public-key cryptography based communication systemcommunicates with another user by means of two different keys, a publickey and a private key. A user's public key and private key form a publickey/private key pair. A message sender communicates securely with amessage recipient by encrypting a message using the recipient's publickey. The sender then sends the message to the recipient who decrypts themessage using the recipient's private key.

The security of messages sent to a user of a public-key basedcryptography system depends on the security of the user's private key.Although the user's public key is freely available to other users, theuser keeps its private key secret and known only to those privileged toreceive messages sent to the user.

The implementation of public key cryptography requires an“infrastructure” to manage requirements such as key distribution and tocertify for key validity. Before encrypting a message to a recipient, amessage sender must have access to the recipient's public key. Thesender must also confirm that this key is valid and not compromised.

In public-key cryptography systems, a trusted third party—the“certification authority” (CA) may perform functions such as keydistribution and certification. Typically, the CA issues a “certificate”for each of its client users together with the CA's electronic signatureto confirm the validity of the certificate. The certificate securelybinds together several quantities. Usually, the certificate includesparameters such as the name of the client and the client's public key.Parameters such as the certificate's issue date and expiration date alsomay be included. By issuing a client's certificate, the CA attests thatthe associated public key is authentic and corresponds to the particularuser for the validity period of the certificate.

Circumstances may require the revocation of a client's certificatebefore its intended expiration date. For example, revocation may benecessary if another party compromises the client's private key.Alternatively, the client may no longer be entitled to use the publickey. If a certificate is revocable, then other users cannot rely on thatcertificate unless the CA distributes certification status informationindicating that a certificate is currently valid. Such information mustbe up to date and distributed to all relying parties. Distributing suchlarge amounts of information requires significant resources on the partof the CA and is a barrier to the widespread implementation ofpublic-key cryptography.

The most well known—but inefficient—public-key infrastructure (PKI)proposal to address the key revocation issue is a certificationrevocation list (CRL). A CRL is a list of certificates revoked beforetheir intended expiration date. The CA issues this list periodicallytogether with its signature to confirm the validity of the CRL. Sincethe CA may revoke many certificates before their intended expirationdate, the CRL may become very long, particularly if the CA has manyclients. Each party requesting a certificate status check receives thislist. Refinements to this approach require transmission of only thosecertificates revoked since the CA's last update. However, thetransmission and infrastructure costs are still high.

An alternative proposal is the Online Certificate Status Protocol(OCSP). In this protocol, any user can query the CA as to the status ofany client of the CA, including the validity of the client's public key.The CA responds to each query by generating a fresh signature on thecertificate's current status. This proposal reduces transmission coststo a single signature per query. However, computation costs increasebecause a fresh signature is required in response to every query.Security also decreases because, if the CA is centralized, it becomesmore vulnerable to denial-of-service (DoS) attacks.

A more promising protocol is the Micali “Novomodo” system. (S. Micali,Efficient Certificate Revocation, Proceedings of RSA Data SecurityConference 1997; S. Micali, Novomodo: Scalable Certificate Validationand Simplified PKI Management, PKI Research Workshop, 2002.) TheNovomodo system involves a CA, one or more directories to distributecertificate information, and the users. However, it achieves betterefficiency than CRLs and OCSP, without sacrifices in security. Theadvantage of Novomodo over a CRL-based system is that a directory'sresponse to a certificate status query is concise compared to a CRLprotocol whereas the length of a CRL grows with the number ofcertificates revoked. Novomodo has several advantages over OCSP. First,the CA's computational load is much lower. Second, unlike thedistributed components of an OCSP, the directories in Novomodo need notbe trusted. Third, Novomodo is less susceptible to DoS attacks. Finally,although the directory-to-user communication costs of OCSP are low,Novomodo's are typically even lower. However, Novomodo still requirescertification status queries.

Many refinements to protocols involving certificate status queriesattempt to reduce PKI computation and transmission requirements andoffer a variety of tradeoffs. However, there are several reasons foreliminating, or at least reducing, certificate status inquiries. First,such inquiries may come from any user and concern any client. Hence,every CA server in the system must be able to determine the certificatestatus for every client of the CA. Second, certificate status queriesfrom the client multiply the query processing costs of the CA. If eachof N clients queries the status of 10 other clients each day, the CAmust process 10N queries. Third, nonclient queries are undesirable froma business model perspective. It is unclear, economically, how the CAshould handle queries from non-clients. Finally, as mentioned above, ifthe CA must respond to queries from non-clients, it becomes moresusceptible to DoS attacks.

Identity-based cryptosystems eliminate third-party queries.Identity-based cryptosystems are public key cryptosystems in which thepublic key of a user derives from the user's identity (name, address,email address, IP address, etc.). A trusted third party generates auser's private key using the user's identity and a master secret held bythe trusted third party. In such a system, a first user can encrypt amessage to the second user without obtaining explicit information otherthan the second user's identifying information and parameters of thesecond user's CA. The second user can decrypt the message only if thatuser has received an updated private key from its CA.

The concept of an identity-based cryptosystem was proposed in A. Shamir,Identity-Based Cryptosystems and Signatures Schemes, ADVANCES INCRYPTOGRAPHY—CRYPTO '84, Lecture Notes in Computer Science 196 (1984),Springer, 47-53. However, practical identity-based encryption schemeshave not been found until recently. For instance, identity-based schemeswere proposed in C. Cocks, An Identity-Based Encryption Scheme Based onQuadratic Residues, available ath-t-t-p://www.cesg.gov.uk/technology/id-pkc/media/ciren.pdf; D. Boneh,M. Franklin, Identity Based Encryption from the Well Pairing, ADVANCESIN CRYPTOLOGY—CRYPTO 2001, Lecture Notes in Computer Science 2139(2001), Springer, 213-229; and D. Boneh, M. Franklin, Identity BasedEncryption from the Well Pairing (extended version), available ath-t-t-p://www.cs.stanford.edu/˜dabo/papers/ibe.pdf. Cocks' scheme isbased on the “Quadratic Residuosity Problem,” and although encryptionand decryption are reasonably fast (about the speed of RSA), there issignificant message expansion (i.e., the bit-length of the ciphertext ismany times the bit-length of the plaintext). The Boneh-Franklin schemebases its security on the “Bilinear Diffie-Hellman Problem,” and it isquite fast and efficient when using Weil or Tate pairings onsupersingular elliptic curves or abelian varieties.

Existing identity-based cryptosystems, however, have had only limitedacceptance. One major reason for this is that these systems involve keyescrow. The CA knows all secrets in the cryptosystem because itgenerates the private keys of all users. As a result, existingidentity-based cryptosystems have been vulnerable to passive attacks inwhich the CA, or any other party that discovers the master secret candetermine shared secret of the two users.

There is a need for an efficient scheme allowing a recipient user of acryptosystem to decrypt a secret message from a message sender only whena trusted third party certifies that the recipient holds a valid privatekey. Ideally, such a scheme should not require that the message senderquery another party, including the third party, as to the status of therecipient's private key. Neither should such a scheme have thedisadvantage of third party key escrow.

It therefore is an object of the present invention to provide anefficient protocol, not involving key status queries or key escrow,wherein a message recipient can decrypt a message from a message senderonly if the recipient obtains authorization (e.g. up to datecertification) from a third party. It is a further object of the presentinvention to provide such a protocol wherein the recipient's decryptionability is contingent upon authorization by several parties. Anotherobject of the present invention is to provide such a protocol whereinthe third party comprises a hierarchical authorization entity within thecryptosystem. It is yet another object of the present invention toprovide an efficient method of providing a user with a private keyhaving a short validity period. It is a further object of the inventionto provide such a protocol that allows such communication in a systemcomprising a large number (e.g. millions) of users.

BRIEF SUMMARY OF THE PREFERRED EMBODIMENTS

The present invention provides methods for implementing a secure andpractical certificate-based encryption scheme.

According to one aspect of the present invention, the method providesfor encoding and decoding a digital message between a sender and arecipient in a public-key encryption scheme including the sender, therecipient and an authorizer. The method includes the steps of generatinga recipient public key/recipient private key pair and a recipientencryption key. A key generation secret that is a secret of theauthorizer is selected. A recipient decryption key is generated using atleast the key generation secret and the recipient encryption key where akey formed from the recipient decryption key and a key formed from therecipient encryption key are a public key/private key pair.

The digital message is encrypted using at least the recipient public keyand the recipient encryption key to create an encrypted digital message.The encrypted digital message is decrypted using at least the recipientprivate key and the recipient decryption key.

Another aspect of the present invention provides a method for sending adigital message between a sender and a recipient in a public-keyencryption system including a plurality of authorizers, the plurality ofauthorizers including at least a root authorizer and a lower-levelauthorizer in a hierarchy between the root authorizer and the recipient.The method includes the steps of generating a recipient publickey/private key pair and a recipient encryption key, where the recipientencryption key is generated using identity information of at least oneof the recipient's ancestors.

A root key generation secret is selected and a root key generationparameter generated based on the root key generation secret. A recipientdecryption key is then generated such that the recipient decryption keyis related to the recipient encryption key, the root key generationsecret and the associated root key generation parameter.

The digital message is encrypted using the recipient public key and arecipient encryption key to create an encrypted digital message, where akey formed from the recipient decryption key and a key formed from therecipient encryption key are a public key/private key pair. Theencrypted digital message is decrypted using at least the recipientprivate key and the recipient decryption key.

Another aspect of the present invention provides a method of generatinga decryption key for an entity in an encryption system including aplurality of authorizers, the plurality of authorizers including atleast a root authorizer and lower-level authorizers in the hierarchybetween the root authorizer and the entity. The method included thesteps of generating a root key generation secret and a root keygeneration parameter based on the root key generation secret. Alower-level key generation secret for the lower-level authorizers isgenerated. A lower-level key generation parameter for lower-levelauthorizers is then generated using at least the lower-level keygeneration secret for its associated lower-level authorizer.

A decryption key generation schedule is established defining a validityperiod for a decryption key for the entity. The decryption key for theentity is generated such that the decryption key is related to at leastthe root key generation secret and one or more of the lower-level keygeneration secrets.

Another aspect of the present invention provides a method of sending adigital message between a sender and a recipient in a public-keyencryption scheme including the sender, the recipient and a plurality ofauthorizers, where the recipient can decrypt the digital message only ifit possesses authorization from the authorizers. The method includes thesteps of generating a recipient public key/private key pair for therecipient and a secret key for each of the authorizers. A public key isgenerated for each of the authorizers using at least the secret key forits associated authorizer. A string of binary digits is signed with thesecret key to generate a signature for each of the authorizers.

The digital message is encrypted to form a ciphertext using at least therecipient's public key, the public keys of the authorizers, and thestrings of binary digits signed by the authorizers. The encrypteddigital message is decrypted using at least the recipient's private key,and the signatures generated by the authorizers.

Another aspect of the present invention provides a method of sending adigital message between a sender and a recipient in a public keyencryption scheme comprising the sender, the recipient and a pluralityof authorizers including at least a root authorizer and lower-levelauthorizers in the hierarchy between the root authorizer and therecipient, where the recipient can decode the digital message only if itpossesses authorization from the authorizers. The method includes thesteps of generating a recipient public key/private key pair for therecipient and a secret key for the root authorizer and each of the lowerlevel authorizers. A public key is generated for the root authorizer andeach of the lower level authorizers using at least the secret key forthe associated authorizer.

Documents, each containing the public key of each of the lower levelauthorizers, are certified to generate a signature, where the documentcontaining the public key of each lower level authorizer is certified bythe authorizer above it in the hierarchy. A document comprising therecipient public key and a parameter determining the validity of therecipient public key is certified by the authorizer immediately abovethe recipient in the hierarchy.

The digital message is encrypted to form a ciphertext using at least therecipient's public key, the public keys of the authorizers, and thedocuments. The encrypted digital message is decrypted using at least therecipient's private key and the signatures generated by the authorizers.

Another aspect of the present invention provides a method of encryptingand decrypting a digital message between a sender and a recipient in apublic-key encryption scheme including the sender, the recipient and anauthorizer. The method includes the steps of generating a recipientpublic key/recipient private key pair and selecting a key generationsecret known to the authorizer. A recipient decryption key associatedwith time period i is generated, where this key is related to the keygeneration secret and where recipient decryption keys associated withtime periods earlier than i, but not those associated with time periodslater than i, can be generated from the recipient decryption keyassociated with time period i.

The digital message is encrypted to form a ciphertext using therecipient public key, the time period parameter associated with timeperiod i or a time period parameter associated with an earlier timeperiod, and a recipient encryption key to create an encoded digitalmessage. The encrypted digital message is decrypted using at least therecipient private key and the recipient decryption key associated withtime period i.

Another aspect of the present invention provides a method of sending adigital message between a sender and a recipient in a public-keyencryption scheme including the sender, a plurality of clients includingthe recipient, and an authorizer, where the digital message is encryptedby the sender and decrypted by the recipient when the recipient isauthorized to do so by the authorizer. The method includes the steps ofgenerating a recipient public key/recipient private key pair and aunique binary string associating the recipient with a leaf node in aB-tree. A unique binary string associated with each ancestor node of therecipient leaf node and an encryption key for the recipient leaf nodeand for each of the ancestor nodes for the recipient leaf node are alsogenerated, as is a master secret known to the authorizer. The encryptionkey for each node is associated with at least the binary stringassociated with that node.

A recipient decryption key associated with an ancestor node of therecipient leaf node is generated, where the ancestor node is not anancestor of a leaf node associated with a client not authorized by theauthorizer. The recipient decryption key is associated with at least thebinary string associated with that node and the master secret. Therecipient decryption key associated with an ancestor node of therecipient leaf node forms a private key/public key pair with theencryption key associated with the ancestor node of the recipient leafnode.

The sender encrypts the digital message to create an encrypted digitalmessage using at least the recipient public key, and the encryption keysassociated with the recipient leaf node and ancestor nodes of therecipient leaf node. The recipient decrypts the encrypted digitalmessage using at least the recipient private key and the recipientdecryption key associated with an ancestor node of the recipient leafnode.

BRIEF DESCRIPTION OF THE DRAWINGS

The subsequent description of the preferred embodiments of the presentinvention refers to the attached drawings, wherein:

FIG. 1 shows a flow diagram illustrating the steps performed by amessage recipient according to one embodiment of the invention;

FIG. 2 shows a flow diagram illustrating the steps performed by anauthorizer according to one embodiment of the invention;

FIG. 3 shows a flow diagram illustrating the steps performed by amessage sender according to one embodiment of the invention;

FIG. 4 shows a flow diagram illustrating a HierarchicalCertificate-Based Encryption scheme according to another embodiment ofthe invention;

FIG. 5 shows a flow diagram illustrating another HierarchicalCertificate-Based Encryption scheme according to an embodiment of theinvention;

FIG. 6 shows a block diagram illustrating a typical hierarchicalstructure in which the method of FIG. 5 may be performed;

FIG. 7 shows a flow diagram illustrating a method of encoding anddecoding a digital message M communicated between a sender y and arecipient z according to another embodiment of the invention;

FIG. 8 shows a flow diagram illustrating a method of encoding anddecoding a digital message M;

FIG. 9 shows a flow diagram illustrating a method of encoding anddecoding a digital message M communicated between a sender y and arecipient z according to another embodiment of the invention.

FIG. 10 shows a diagram illustrating a High-Granularity EncryptionScheme.

FIG. 11 shows a flow diagram illustrating a broadcast encryption schemeusing a binary tree.

FIG. 12 shows a block diagram illustrating broadcast encryption schemeusing the cover concept.

DESCRIPTION OF THE EMBODIMENTS

The methods of the invention provide efficient protocols allowing asender in a cryptosystem to communicate a secret message to a recipientonly when a trusted third party (the “authorizer”) certifies that therecipient should receive the message.

In the protocols described below, the names “sender” and “recipient”represent two users of a cryptosystem. Such a cryptosystem may includemany users other than the sender and recipient. Specifically, the senderrepresents a first user who wishes to communicate a secret message to asecond user, represented by the recipient. The message may contain anytype of digital information, including session keys used with symmetriccryptography algorithms to secure message traffic.

The term “Certification Authority (CA)” represents the entityresponsible for managing the public-key infrastructure of thecryptosystem. The major functions of the CA may include the generationand distribution of digital certificates as well as public keys. The CAmay be a single entity or may consist of a distributed or hierarchicalstructure of entities.

The term “authorizer” represents a third party trusted by a messagesender using the cryptosystem to certify that a message recipient hasauthority to receive a message encrypted to a message recipient. Theauthorizer may be a single entity or may consist of a distributed orhierarchical structure of entities. In many systems, the authorizer andthe CA will be the same entity. However, this will not always be so. Themessage recipient's ability to decrypt a message can be contingent onauthorization from any specified entity or entities.

The term “certificate” represents an identifier used by individual usersof the cryptosystem to identify and authenticate themselves to otherusers. A certificate has certain attributes that enable users to trustthe information contained in the certificate. Typically, a certificateconsists of a digital signature on a document containing informationsuch as the identity of the certificate owner, the public key of thecertificate owner, the identity of the CA, an issue date, an expirationdate, a serial number, and a parameter allowing users to verify that thecertificate is genuine and valid. To verify the certificate, theverifier must know the document signed. This information is often sentwith the certificate

The term “public-key cryptosystem” represents a cryptosystem wherein asender sends an encrypted message to a recipient. The sender encryptsthe message using the recipient's public key. The recipient decrypts theencrypted message using the recipient's private key. Such a public keyand private key form a “public key/private key pair”. It iscomputationally infeasible to determine the recipient's private key fromknowledge of the recipient's public key. Examples of public-keycryptosystems are the RSA Cryptosystem, in which the security of theprivate key is related to the difficulty of factoring large integers,and the EIGamal Cryptosystem, in which the security of the private keyis related to the discrete logarithm problem. The term “form a publickey/private key pair” will be understood by those skilled in the art toinclude a situation where the definitions of the public and private keysare redefined but the overall ability of the keys to encrypt and decryptmessages in maintained.

The terms “tree” and “B-tree” represent data structures that maintain anordered set of data. A B-tree consists of “nodes”, “leafs”, and pointersconnecting the nodes and leafs together. A “root node” defines the base,or first level, of the B-tree. A pointer connects the root node to eachof a second level of nodes. The second level nodes are the child nodesof the root node. The root node is the parent node of the second levelnodes. Further pointers may connect each of the second level nodes totheir own child nodes and so on. “Leaf” nodes are the highest level ofnodes of the B-tree. The leaf nodes are the child nodes of the next tohighest level nodes and have no children of their own. Those nodesconnecting a node to the root node, including the root node itself, aretermed the ancestor nodes of this node.

The term “binary tree” represents a B-tree in which every node, exceptthe leaf nodes, has at most two children.

The term “2-3 tree” represents a B-tree in every interior node has twoor three children.

The term “Merkle tree” represents a B-tree whose nodes store values,some of which computed by means of a one-way function H, for example, aone-way hash function, in a specified manner. A leaf node can store anyvalue, but each internal node should store a value that is the one-wayfunction of the concatenation of the values in its children. Forexample, if an internal node has a two children, one storing the value Uand the other storing a value V, then this node stores the value H(UV)).

Certificate-Based Encryption

The present invention describes “certificate-based encryption (CBE)”schemes where the ability of a message recipient user of a cryptosystemto decrypt a secret message from a message sender is contingent on theauthorization of one or more trusted authorizers. The message recipientneeds at least two keys to decrypt a message. One of these keys is asignature by one or more authorizers on one or more documents. The CBEprotocols of the invention include a public-key encryption scheme and anadapted Identity-Based Encryption (IBE) scheme. Such protocols allow forCBE schemes including large numbers of users (e.g. millions of users)without destroying the algebraic structure necessary for CBE. In theprotocols described below, a sender communicates an encrypted message toa recipient.

In the public-key encryption scheme, an entity, e.g. the recipient,generates a public key/private key pair (PK_(B), SK_(B)) for therecipient. The recipient's public key is available to other users of thecryptosystem, including the sender. The other users can use this key toencrypt messages sent to the recipient. The recipient keeps therecipient private key secret and uses this key to decrypt messagesencrypted with the recipient's public key.

A CBE protocol may incorporate any IBE scheme. An IBE scheme uses atrusted third party called a Private Key Generator (PKG). To set up, thePKG generates a master secret s, and publishes certain system parametersparams that include a public key that masks s. The PKG may have manyclients. Each client has some ID, which is simply a string thatidentifies it—e.g., the client's email address. The main algorithms inan IBE scheme are Private Key Generation, Encryption, and Decryption.

In the Private Key Generation algorithm, the PKG uses s, params and IDto compute a private key d_(ID) corresponding to a given ID string. Themessage sender then uses the Encryption algorithm to compute theciphertext C for the message M, using params, ID, and M. The messagerecipient used params, d_(ID), and C to recover M.

In an IBE scheme adapted to implement a CBE scheme, the authorizergenerates a recipient “decryption key” using a key generation secretthat is a secret of the authorizer. The decryption key forms a publickey/private pair with a recipient “encryption” key. In one embodiment,the recipient decryption key is a signature on the recipient encryptionkey generated using the key generation secret. The message senderencrypts a digital message using the recipient public key and therecipient encryption key to create an encrypted digital message. Therecipient decrypts the encrypted digital message using the recipientprivate key and the recipient decryption key. Since the sender encryptsthe message using both the recipient public key and the recipientencryption key, the recipient needs both the recipient private key andrecipient decryption key to decrypt the encrypted message. Because bothkeys are required, the recipient decryption key need not be kept secret.For example, since the recipient decryption key is in fact a signatureby one or more authorizers, the decryption can be treated as asignature; it can be used as verifiable proof that the recipient hasreceived appropriate authorization.

In general, the encryption key can correspond to a document D and thedecryption key to the signature s_(D), the authorizer's signature on thedocument D using s, the authorizer's key-generation secret. If thedecryption key, and hence the encryption key, are updated using aschedule known to the message sender, the sender can encrypt a messagethat the recipient can decrypt only when the recipient receives adecryption key corresponding to the encryption key used to encrypt themessage.

The above scheme reduces the infrastructure overhead on the cryptosystemby avoiding the need for the sender to query to ensure that therecipient's private key is not compromised. The sender merely must knowencryption key and the schedule on which the authorizer issues a newdecryption key to the recipient. Without an up-to-date decryption key,an attacker knowing the recipient's private key cannot decrypt messagesintended for the recipient. Thus, the CBE scheme allows the recipient'sauthorization to decrypt messages to be revoked if, for example, therecipient's private key is compromised. In such a situation, theauthorizer stops issuing decryption keys to the recipient.

The scheme offers the additional advantage that it does not require thetransmission of decryption keys to the recipient over a secure channel.Because decryption is not possible without the recipient's private keyand the decryption key, the recipient need not keep the decryption keysecret.

Because the authorizer knows the decryption key, it can decrypt messagesencrypted by the encryption key. However, the sender avoids key escrowby doubly encrypting messages to the recipient using both therecipient's public key and encryption key. The authorizer cannot decryptthe message because it does not know the recipient's private key.

Although the encryption key can correspond to any document D, in manysituations this document comprises parameters such as the recipient'sidentifying information (PK_(IDB)), including the recipient's public key(PK_(B)), and a parameter depending on the schedule by which theauthorizer issues new decryption keys.

In a CBE scheme, the recipient's encryption key, the recipient's publickey, and a parameter describing the schedule by which the authorizerissues new decryption keys are distributed to users of the cryptosystem,including the sender. The recipient can perform this function.Alternatively, a trusted third party, for example the CA or theauthorizer, may perform the distribution.

Validity Period and Revocation

If the sender encrypts a message to the recipient using an encryptionkey that is valid for the current year, the recipient may use thecorresponding decryption key for decryption during the current year.After this period, the recipient must obtain a new key from theauthorizer. Likewise, if the sender encrypts a message using anencryption key that is valid for the current day, the recipient mustobtain a new decryption key every day. Using this approach, a system maybe created in which key revocation is automatic after any particulardesired time-period. Similarly, the structure of the encryption may besuch that the recipient can decrypt a message from a sender only at apre-determined future time.

Other parameters, such as the recipient's security level, may also beincluded in the encryption key. If the sender encrypts a message usingboth a time parameter and a security level parameter, the recipient candecrypt the message only if the recipient has an up-to-date decryptionkey that specifies the required security level parameter. If therecipient's security level changes, the recipient will not be able todecrypt the sender's message.

A Pairing-Based CBE Scheme

A CBE scheme may incorporate any IBE scheme. Examples of such schemesare those based on Weil or Tate pairings associated with elliptic curvesor abelian varieties. One embodiment of a CBE scheme of the presentinvention is described below. This embodiment uses the Boneh-FranklinIBE scheme and an identity-based encryption key comprising parameterssuch as the recipient's identifying information (PK_(IDB)), includingthe recipient's public key (PK_(B)), and a parameter depending on theschedule by which the authorizer issues new decryption keys. Thisembodiment is efficient and is provably secure (in the random oraclemodel) against adaptive chosen ciphertext attack.

Referring to the accompanying drawings, FIG. 1 shows a flow diagramillustrating the steps taken by a message recipient during a setupphase. This setup phase occurs before the recipient decrypts anencrypted message. In block 101, the recipient generates a publickey/private key pair using a public-key cryptography protocol. In block102, the recipient generates identifying information. In block 103, therecipient communicates identifying information, including therecipient's public key, to other users, including the message sender,and the authorizer.

FIG. 2 shows a flow diagram illustrating the steps taken by theauthorizer during parameter setup and recipient certification. As usedin the CBE scheme, the Boneh-Franklin IBE scheme generally includes fourrandomized algorithms: setup, certification, encryption, and decryption.Here, the authorizer is the equivalent of the Private Key Generator(PKG) in the conventional IBE scheme.

During setup, the authorizer uses a BDH parameter generator and asecurity parameter k to generate groups

₁ and

₂ of some prime order q and an admissible pairing ê:

₁×

₁→

₂. The pairing is defined as being admissible if it is bilinear: ê(aQ,bR)=ê(Q, R)^(ab) for all Q, R∈

₁ and all a, b∈

; non-degenerate: the mapping does not send all pairs in

₁×

₁ to the identity in

₂; and computable: there is an efficient algorithm to compute ê(Q, R)for any Q, R∈

₁.

The Boneh-Franklin IBE scheme based on pairings, such as, for instance,the Weil or Tate pairings associated with elliptic curves or abelianvarieties. The methods base their security on the BilinearDiffie-Hellman problem. Here, the first group

₁ preferably is a group of points on an elliptic curve or abelianvariety, and the group law on

₁ may be written additively. The second group

₂ preferably is a multiplicative subgroup of a finite field, and thegroup law on

₂ may be written multiplicatively. However, other types of groups may beused as

₁ and

₂ consistent with the present invention.

The Bilinear Diffie-Hellman problem is that of finding ê(P, P)^(abc) ifP, aP, bP, and cP are known, but a, b, and c are not known. Solving theDiffie-Hellman problem in

₁ solves the Bilinear Diffie-Hellman problem because ê(P,P)^(abc)=ê(abP, cP). Similarly, solving the Diffie-Hellman problem in

₂ solves the Bilinear Diffie-Hellman problem because, if g=ê(P, P), theng^(abc)=(g^(ab))^(c) where g^(ab)=ê(aP, bP) and g^(c)=ê(P, cP). Forinstance, suppose E is a supersingular elliptic curve or abelian varietyover a finite field F; suppose P∈E(F) is a point of order l (relativelyprime to the characteristic of F); and suppose ê is the Weil pairing onthe l-torsion on E. Let

₁ be the group generated by P, and let

₂ be the group of l-th roots of unity in the algebraic closure of F. Iff is an automorphism of E such that f(P)∉

₁, then defining ê:

₁×

₁→

₂ by ê(Q, R)=e(Q, f(R)) gives a function ê that satisfies the twoconditions set forth above. Further, this ê is non-degenerate. Forinstance, if ê(aP, bP)=ê(P, cP), then abP=cP.

In blocks 201 and 202 of FIG. 2, the authorizer selects a key generationsecret and establishes system parameters by choosing an arbitrarygenerator P∈

₁, picking a random s_(c)∈

/q

, setting Q=s_(c)P, and choosing cryptographic functions H₁: {0,1}*→

₁, H_(1′): {0,1}*→

G₁ and H₂:

₂→{0,1}^(n) for some n. Here, the message space is

={0,1}^(n), the system parameters are params=(

₁,

₂, ê, P, Q, H₁, H_(1′), H₂), and the authorizer's master key generationsecret is s_(c)∈

/q

.

In block 203, the authorizer certifies identifying information sent bythe recipient, including the recipient's public key s_(B)P where s_(B)is the recipient's private key. In block 204, the authorizer establishesa schedule updating the recipient's identity-based decryption key. Ifverification is satisfactory, the authorizer generates theidentity-based decryption key. The authorizer computesP_(B)=H₁(Inf_(B))∈

₁, where Inf_(B) includes the recipient's identifying information(including the public key) and ancillary information such as a validityperiod, and P′_(B)=H_(1′)(ID_(rec)), where ID_(rec) comprises the publickey of the recipient. In block 205, the authorizer then computes therecipient's identity-based decryption key s_(c)P_(B) and sends thisinformation to the recipient. The authorizer may also distribute therecipient's identifying information to other users as in block 206.Alternatively, another entity may perform this function.

FIG. 3 shows a flow diagram illustrating the steps taken by the senderduring encryption of a message. In blocks 301 and 302, the messagesender obtains the recipient's public key and the system parameters. Inblock 303, the sender obtains the recipient's identity-based encryptionkey comprising the recipient's identifying information and the ancillaryinformation, including the authorizer's identity-based decryption keygeneration schedule.

In block 304, the sender doubly encrypts the message M∈

with both s_(B)P and Inf_(B) as follows. Initially, the sender computesP_(B)=H₁(Inf_(B))∈

₁, P′_(B)=H_(1′)(ID_(rec)), wherein ID_(rec) comprises the public key ofthe recipient, and then chooses a random r∈

/q

. The sender then sets the ciphertext to be:C=[rP, M

H ₂(g ^(r))], where g=ê(Q, P _(B))ê(s _(B) P, P′ _(B))∈

₂In block 305, the sender sends the message to the recipient.

Let the ciphertext received by the recipient be C=[U,V]. Duringdecryption, the recipient recovers M using SK_(B) and s_(c)P_(B).Specifically, the recipient first computes S_(B)=s_(C)P_(B)+s_(B)P′_(B)and then computes:V

H ₂(ê(U, S _(B)))=M.

CBE can be made secure in the random oracle model against adaptivechosen-ciphertext attack by using, for example, the Fujisaki-Okamototransform in a manner similar to that described for IBE by D. Boneh, &M. Franklin, (2001). The transformed scheme uses two additionalcryptographic functions H₃ and H₄ and a semantically symmetricencryption scheme E_(H) ₄ _((σ)). H₃ is a function capable of generatingan integer of the cyclic group

/q

from two strings of binary digits and H₄ is a function capable ofgenerating one binary string from another binary string. H₄(σ) is thekey used with E.

In the transformed scheme, the message sender chooses a randomσ∈{0,1}^(n) and sets r=H₃(σ,M). The sender then sets the ciphertext tobe: C=[rP,σ

H₂(g^(r)), E_(H4(σ))M] where g=ê(Q, P_(B))ê(s_(B)P, P′_(B))∈

₂.

The message recipient decrypts [U,V,W] by computing σ=V

H₂(ê(U,s_(C)P_(B))) and M=H⁻¹ _(H4(σ))(W). The recipient also setsr=H₃(σ,M) and rejects the ciphertext if U≠rP.

Hierarchical CBE

In yet another embodiment of the present invention, a CBE schemecombines a Hierarchical Identity Based Encryption (HIDE) scheme and apublic-key encryption scheme. As in the non-hierarchical schemediscussed above, the encryption key can correspond to any document D. Inthe following description, the key is comprised of parameters such asthe recipient's identifying information (PK_(IDB)), including therecipient's public key (PKB), and a parameter describing the schedule bywhich the authorizer issues new decryption keys.

A hierarchical identity-based key sharing scheme with partialcollusion-resistance is described in G. Hanaoka, T. Nishioka, Y. Zheng,H. Imai, An Efficient Hierarchical Identity-Based Key-Sharing MethodResistant Against Collusion Attacks, Advances in Cryptography—Asiacrypt1999, Lecture Notes in Computer Science 1716 (1999), Springer 348-362;and G. Hanaoka, T. Nishioka, Y. Zheng, H. Imai, A HierarchicalNon-Interactive Key-Sharing Scheme With Low Memory Size and HighResistance Against Collusion Attacks, to appear in The Computer Journal.In addition, an introduction to hierarchical identity-based encryptionwas provided in J. Horwitz, B. Lynn, Toward Hierarchical Identity-BasedEncryption, to appear in Advances in Cryptography—Eurocrypt 2002,Lecture Notes in Computer Science. Springer. Horwitz and Lynn proposed atwo-level hierarchical scheme with total collusion-resistance at thefirst level and partial collusion-resistance at the second level (i.e.,users can collude to obtain the secret of their domain PKG andthereafter masquerade as that domain PKG). However, the complexity ofthe Horwitz-Lynn system increases with the collusion-resistance at thesecond level, and the scheme therefore cannot be both practical andsecure.

Secure and practical HIDE schemes are described in U.S. patentapplication Ser. No. 10/384,328 (now U.S. Pat. No. 7,349,538, issued onMar. 25, 2008), the contents of which are incorporated herein for allpurposes by this reference.

The present hierarchical CBE (HCBE) scheme adapts the HIDE scheme toCBE, and it includes six randomized algorithms: Root Setup, Lower-levelSetup, Certification, Extraction, Encryption, and Decryption. Four ofthese algorithms rely upon the identities of the relevant entities inthe hierarchy. Each user preferably has a position in the hierarchy thatmay be defined by its tuple of IDs: (ID₁, . . . , ID_(t)). The user'sancestors in the hierarchy are the root authorizer and the lower levelauthorizers whose ID-tuples are {(ID₁, . . . , ID_(i)): 1≦i≦t−1}.Preferably, binary strings represent the ID-tuples for purposes ofcomputations.

The Root Setup algorithm is similar to that for the non-hierarchicalscheme described above. The root authorizer uses a security parameter kto generate public system parameters params and a root key generationsecret in the same manner as the authorizer in a non-hierarchicalscheme. Again, the system parameters will be publicly available, butonly the root authorizer will know the root key generation secret.

In the Lower-level Setup algorithm, lower-level authorizers may retrievethe system parameters from the root authorizer. Unlike the rootauthorizer, the lower-level authorizers do not have “lower-level”parameters used in the Encryption algorithm. However, this constraintdoes not necessarily preclude a lower-level authorizer from generatingits own lower-level secret, which it may use to generate and issueidentity-based decryption keys to its users. A lower-level authorizermay generate its own lower-level key generation secret for purposes ofextraction. Alternatively, a lower-level authorizer may generate randomone-time secrets for each extraction.

In the Extraction algorithm, a parent authorizer (whether the rootauthorizer or a lower-level authorizer) verifies identifying informationsent by a child authorizer immediately below it in the hierarchy. Theparent authorizer may also establish a schedule for update of the childauthorizer's recipient's identity-based decryption key. If verificationis satisfactory, the parent authorizer generates an identity-baseddecryption key for the child authorizer. As in the non-hierarchicalscheme, this identity-based decryption key is generated using the systemparameters, the child authorizer's identifying information and ancillaryinformation such as a validity period. The child authorizer'sidentity-based decryption key is also related to the key generationsecret of at least one ancestral authorizer. The parent authorizer thensends this decryption to the child authorizer. The child authorizer'sidentifying information is available to other users.

In the Certification algorithm, a signing authorizer having at least oneancestor in the hierarchy certifies identifying information sent by therecipient, including the recipient's public key PK_(B). The authorizeralso establishes a schedule for update of the recipient's identity-baseddecryption key. If verification is satisfactory, the authorizergenerates an identity-based decryption key SK_(HIDB) for the recipient.As in the non-hierarchical scheme, key SK_(HIDB) is generated using thesystem parameters, the recipient's identifying information (includingthe public key) and ancillary information such as a validity period.SK_(HIDB) is also related to the key generation secret of at least oneancestral authorizer. The authorizer then sends key SK_(HIDB) to therecipient. The recipient's identifying information Inf_(B) is availableto other users.

In the Encryption algorithm, a sender doubly encodes a message M to anintended recipient using both the intended recipient's public key PK_(B)and params and the recipient's identity-based encryption key, comprisinginformation included in Inf_(B) and the ID-tuple of the intendedrecipient.

Conversely, in the Decryption algorithm, the recipient decodes theciphertext C to recover the message M using the recipient's private keySK_(B) and identity-based decryption key (SK_(HIDB)).

Pairing Based Hierarchical CBE

One embodiment of the HCBE scheme of the present invention is based onpairings, such as, the Weil or Tate pairings associated with ellipticcurves or abelian varieties, and on the Bilinear Diffie-Hellman problemdescribed above.

FIG. 4 shows a flow diagram illustrating a method of encoding anddecoding a digital message in a HIDE system including a plurality ofauthorizers according to one embodiment of the invention. Theauthorizers include at least a root authorizer and n lower-levelauthorizers in the hierarchy between the root authorizer and therecipient, wherein n≧1. In block 402, the root authorizer selects a rootkey generation secret known only to the root authorizer. The rootauthorizer then generates a root key generation parameter based on theroot key generation secret in block 404. The lower-level authorizersselect lower-level key generation secrets in block 406. Like the rootkey generation secret, each of the lower-level key generation secrets isknown only to its associated lower-level authorizer. In block 408,lower-level key generation parameters are generated for each of the nlower-level authorizers. Each of the lower-level key generationparameters is generated using at least the lower-level key generationsecret for its associated lower-level authorizer. Like the root keygeneration parameter, each of the lower-level key generation parametersmasks its associated lower-level key generation secret.

Using at least one of the key generation parameters and the recipientidentity-based encryption key, the sender encodes the message in block410 to form a ciphertext. For instance, the sender may encode themessage using only the root key generation parameter and the recipient'spublic key. Alternatively, the sender may use one of the lower-level keygeneration parameters, as described in more detail below with respect todual-HCBE schemes. In block 412, a lower-level authorizer generates anidentity-based decryption key for the recipient such that theidentity-based decryption key is related to at least one of the nlower-level key generation secrets. For instance, the recipient'sidentity-based decryption key preferably is related at least to thelower-level key generation secret of the authorizer that issued theidentity-based decryption key to the recipient. Alternatively, therecipient's identity-based decryption key may be related to all n of itsancestral authorizer's lower-level key generation secrets, as well asthe root key generation secret. In block 414, the recipient uses atleast its identity-based decryption key and its private key to decodethe ciphertext and recover the message.

Each lower-level authorizer has a key generation secret, just like theroot authorizer. As described above, a lower-level authorizer preferablyuses this secret to generate a private key for each of its children,just as the root authorizer does. However, the lower-level authorizersneed not always use the same secret for each identity-based decryptionkey extraction. Rather, a new key generation secret may be generatedrandomly for each of the authorizer's clients.

Because a lower-level authorizer is able to generate an identity-baseddecryption key for the recipient (block 412), the root authorizer neednot generate all of the identity-based decryption keys itself. Inaddition, because the lower-level authorizers use their own keygeneration secrets to generate identity-based decryption keys for theirclients, compromising a lower-level key generation secret causes onlylimited security damage to the hierarchy. Rather than compromising allof the identity-based decryption keys in the hierarchy, a breach of alower-level authorizer compromises only those identity-based decryptionkeys that were generated using that authorizer's key generation secret(i.e., only the identity-based decryption keys of those users that aredirect hierarchical descendants of the compromised authorizer).

Another advantage of this embodiment is that the sender need not be inthe hierarchy to send an encoded message to the recipient. The sendermerely needs to know the identity of the recipient, the recipient'spublic key and the system parameters generated by the root authorizer.There are, however, certain additional advantages of the HIDE schemes ofthe present invention that become available when the sender is withinthe hierarchy. For instance, when both the sender and the recipient arein the hierarchy, using the identities of both parties improves theefficiency of the message encryption. This type of HCBE scheme is calleddual-HCBE because the identities of both the sender and the recipientare used as input for the encryption and decryption algorithms. A methodof encoding and decoding a message using a dual-HCBE scheme is nowdiscussed with reference to FIGS. 5 and 6.

FIG. 5 shows a flow diagram illustrating a method of encrypting anddecrypting message between a sender y and a recipient z according toanother embodiment of the invention. FIG. 6 shows a block diagramillustrating a typical hierarchical structure. Like the previousembodiment, this method is performed in a HCBE system including at leasta root authorizer 602 and n lower-level authorizers 604 a,b,d in thehierarchy between the root authorizer 602 and the recipient z 608,wherein n≧1. The sender y 606 in this embodiment also must be in thehierarchy, and the hierarchy also includes m lower-level authorizers 604a,b,c between the root authorizer 602 and the sender y 606, wherein m≧1.Of the in authorizers 604 a,b,c between the root authorizer 602 and thesender y 606, and the n authorizers 604 a,b,d between the rootauthorizer 602 and the recipient z 608, there are l authorizers 604 a,bthat are common ancestors to both the sendery 606 and the recipient z608, wherein 1≦l≦m, n. For instance, FIG. 6 shows two of these l commonancestral authorizers (CA_(y1)/CA_(z1) 604 a and CA_(yl)/CA_(zl) 604 b).

The method of this embodiment begins in block 502, when the rootauthorizer 602 selects a root key generation secret known only to theroot authorizer. The root authorizer 602 then generates a root keygeneration parameter based on the root key generation secret in block504. The lower-level authorizers 604 a-d select lower-level keygeneration secrets in block 506. Like the root key generation secret,each of the lower-level key generation secrets is known only to itsassociated lower-level authorizer 604 a-d. In block 508, lower-level keygeneration parameters are generated for each of the n lower-levelauthorizers 604 a-d. Each of the lower-level key generation parametersis generated using at least the lower-level key generation secret forits associated lower-level authorizer 604 a-d.

In block 510, the sender's parent CA_(ym) 604 c generates anidentity-based decryption key for the sender y 606 such that theidentity-based decryption key is related to at least one of the inlower-level key generation secrets associated with the m lower-levelauthorizers 604 a,b,c between the root authorizer 602 and the sender y606. For instance, the sender's identity-based decryption key preferablyis related at least to the lower-level key generation the sender'sparent CA_(ym) 604 c. Alternatively, the sender's identity-baseddecryption key may be related to all m of its direct ancestralauthorizers' lower-level key generation secrets, as well as the root keygeneration secret. The sender's identity-based encryption key cancorrespond to any document D, but, in the following description, the keycomprises parameters such as the sender's identifying information(PK_(IDA)), including the sender's public key (PK_(A)), and a parameterdescribing the schedule by which the authorizer issues new decryptionkeys. In block 512, the recipient's parent CA_(zn) 604 d generates anidentity-based decryption key for the recipient z in a similar mannerthat the sender's parent CA_(ym) 604 c used to generate the sender'sidentity-based decryption key. As in HCBE, the recipient'sidentity-based encryption key can correspond to any document D, but, inthe following description, the key comprises parameters such as therecipient's identifying information (PK_(IDB)), including therecipient's public key (PK_(B)), and a parameter describing the scheduleby which the authorizer issues new decryption keys.

In block 514, the sender y encodes the message to form a ciphertext. Ituses at least the recipient's public key, the sender's identity-baseddecryption key and one or more of the lower-level key generationparameters associated with the (m−l+1) authorizers (i.e., CA_(yl), 604 band CA_(ym) 604 c) between the root authorizer 602 and the sender y 606that are at or below the level of the lowest ancestor authorizer(CA_(yl)/CA_(zl) 604 b) that is common to both the sender y 606 and therecipient z 608. In encoding the message, the sender y 606 preferablydoes not use any of the lower-level key generation parameters that areassociated with the (l−1) authorizers (i.e., CA_(y1) 604 a) that areabove the lowest common ancestor authorizer (CA_(yl)/CA_(zl) 604 b).Again, the lower-level key generation parameters are related to therecipient's identifying information and the ancillary information,including the authorizer's identity-based decryption key generationschedule.

The recipient z 608 then decodes the ciphertext to recover the messagein block 516. It uses at least the recipient's private key, therecipient's identity-based decryption key and one or more of thelower-level key generation parameters associated with the (n−l+1)authorizers (i.e., CA_(zl), 604 b and CA_(zn) 604 c) between the rootauthorizer 602 and the recipient z 608 that are at or below the level ofthe lowest ancestor authorizer (CA_(yl)/CA_(zl) 604 b) that is common toboth the sender y 606 and the recipient z 608. In decoding the message,the recipient y 606 preferably does not use any of the lower-level keygeneration parameters that are associated with the (l−1) authorizers(i.e., CA_(z1) 604 a) that are above the lowest common ancestorauthorizer (CA_(yl)/CA_(zl) 604 b).

The dual-HCBE embodiment of the invention provides a more efficientscheme for encoding and decoding the message because it requires the useof fewer key generation parameters. For instance, decoding in a regularHCBE scheme preferably requires all n of the key generation parameters,decoding in a dual-HCBE scheme preferably requires only (n−l) of the keygeneration parameters. Dual-HCBE schemes require that the sendery 606obtain its identity-based decryption key before sending an encodedmessage to the recipient z 608, as opposed to merely obtaining thepublic system parameters of the root authorizer.

The dual-HCBE schemes also enable the sender y 606 and the recipient z608 to use a limited form of key escrow, as described more fully below.This shared secret is unknown to third parties other than their lowestcommon ancestor CA_(yl)/CA_(zl) 604 b. However, the CBE schemes of thepresent invention avoid key escrow entirely. Nevertheless, dual-HCBEcontinues to offer the advantages of shorter ciphertext length anddecryption time.

FIG. 7 shows a flow diagram illustrating a method of encoding anddecoding a digital message M communicated between a sender y and arecipient z according to another embodiment of the invention. Therecipient z 608 is n+1 levels below the root authorizer in thehierarchy, as shown in FIG. 6, and is associated with the ID-tuple(ID_(zl), . . . , ID_(z(n+1))). The recipient's ID-tuple includesidentity information ID_(z(n+1)) associated with the recipient, as wellas identity information ID_(zi) associated with each of its n ancestrallower-level authorizers in the hierarchy.

The method begins in block 702 by generating the first and second cyclicgroups

₁ and

₂ of elements. In block 704, a function ê is selected such that theadmissible pairing ê is capable of generating an element of the secondcyclic group

₂ from two elements of the first cyclic group

₁. A root generator P₀ of the first cyclic group

₁ is selected in block 706. In block 708, a random root key generationsecret s₀ associated with and known only to the root authorizer 602 isselected. Preferably, s₀ is an element of the cyclic group

/q

. A root key generation parameter Q₀=s₀P₀ is generated in block 710.Preferably, Q₀ is an element of the first cyclic group

₁. In block 712, a first function H₁ is selected such that H₁ is capableof generating an element of the first cyclic group

₁ from a first string of binary digits. For simplicity, only onefunction capable of generating an element of the first cyclic group

G₁ from a first string of binary digits needs to be used, but severaldifferent functions of this type may be used at different points in thealgorithm. A second function H₂ is selected in block 714, such that H₂is capable of generating a second string of binary digits from anelement of the second cyclic group

₂. The functions of blocks 702 through 714 are part of thenon-hierarchical and HCBE Root Setup algorithms described above, and canbe performed at about the same time.

The next series of blocks (blocks 716 through 724) show the functionsperformed as part of Lower-level Setup algorithm. In block 716, aelement P_(zi) is generated for each of the recipients' n ancestrallower-level authorizers. Each of the elements, P_(zi)=H₁(ID_(z1), . . ., ID_(zi)) for 1≦i≦n, preferably is an element of the first cyclic group

₁. Although represented in a single block, generation of all the publicelements P_(zi) may take place over time, rather than all at once.

A lower-level secret s_(zi) is selected (block 720) for each of therecipients' n ancestral lower-level authorizers 604 a,b,d. Thelower-level secrets s_(zi) preferably are elements of the cyclic group

/q

for 1≦i≦n, and each lower-level key generation secret s_(zi) preferablyis known only to its associated lower-level authorizer. Again, althoughrepresented in a single block, selection of all the secrets s_(zi) maytake place over time, rather than all at once.

A lower-level secret element S_(zi) is generated (block 722) for each ofthe recipient's n ancestral lower-level authorizers. Each lower-levelsecret element, S_(zi)=S_(z(i−1))+s_(z(i−1))P_(zi) for 1≦i≦n, preferablyis an element of the first cyclic group

₁. Although represented in a single block like the public elementsP_(zi) and the secrets s_(zi), generation of all the secret elementsS_(zi) may take place over time, rather than all at once.

A lower-level key generation parameter Q_(zi) also is generated (block724) for each of the recipients' n ancestral lower-level authorizers.Each of the key generation parameters, Q_(zi)=s_(zi)P₀ for 1≦i≦n ,preferably is an element of the second cyclic group

₂. Again, although represented in a single block, generation of all thekey generation parameters Q_(zi) may take place over time, rather thanall at once.

The functions of the next two blocks (blocks 726 and 728) are performedas part of the Certification algorithm described above. A recipientelement P_(z(n+1)) associated with the recipient z is generated in block726. The recipient element, P_(z(n+1))=H₁(Inf_(z(n+1)), ID_(z1), . . . ,ID_(z(n))), preferably is an element of the first cyclic group

₁. Here, Inf_(z(n+1)) is a string of binary digits that may include therecipient's public key and ancillary information such as the validityperiod of the recipient's identity-based decryption key. A recipientsecret element S_(z(n+1)) associated with the recipient z is thengenerated in block 728. The recipient decryption keyS_(z(n+1))=S_(zn)+s_(zn)P_(s(n+1))=Σ_(i=1) ^(n+1)s_(z(i−1))P_(zi), alsopreferably is an element of the first cyclic group

₁. Using the recipient decryption key and SK_(B), the recipient computesS_(B)=S_(z(n+1))+s_(B)P′_(B).

For convenience, the first function H₁ optionally may be chosen to be aniterated function so that, for example, the public points P_(i) may becomputed as H₁(P_(z(i−1)), ID_(zi)) rather than H₁ (ID₁, . . . ,ID_(zi)).

The last two blocks shown in FIG. 7 (blocks 730 and 732) represent theEncryption and Decryption algorithms described above. In block 730, thesender encrypts message M to generate a ciphertext C. The encodingpreferably uses at least the recipient's public key and the root keygeneration parameter Q₀. The recipient decrypts ciphertext C in block732 to recover the message M. The decoding preferably uses at least thelower-level key generation parameters Q_(zi) and the recipientdecryption key S_(z(n+1)) and the recipient private key. The specificuse of the parameters and elements in the encoding and decoding of themessage M and the ciphertext C is now discussed with reference to FIGS.8 and 9.

FIG. 8 shows a flow diagram illustrating a method of encoding anddecoding a digital message M communicated between a sender y and arecipient z according to another embodiment of the invention. In thisscheme, referred to as BasicHCBE, the Root Setup, Lower-level Setup,Extraction and Certification algorithms are the same as for theembodiment shown in blocks 702 through 728 of FIG. 7. Accordingly, theflow diagram of FIG. 8 begins with the selection of a random encryptionparameter r in block 830 a. Preferably, r is an integer of the cyclicgroup

/q

. The ciphertext C is then generated in block 830 b using the formulaC=[rP₀, rP_(z2), . . . , rP_(z(n+1)), V], wherein V=M

H₂(g^(r)), wherein g=ê(Q₀, P_(z1))ê(s_(B)P₀, P′_(B)). Here, s_(B)P₀ isthe recipient public key, P′_(B) is H₁(Inf_(rec)), wherein Inf_(rec)comprises the recipient's public key.

After the message has been encoded, it may be decoded according to theBasicHCBE Decryption algorithm, in which the message M is recovered fromthe ciphertext C (block 832) using the formula

$M = {V \oplus {H_{2}( \frac{\hat{e}( {U_{0},S_{n + 1}} )}{\prod\limits_{i = 2}^{n + 1}\;{\hat{e}( {Q_{i - 1},U_{i}} )}} )}}$where C=[U₀, U₂, . . . , U_(n+1), V].

Known methods for making one-way encryption schemes secure againstchosen-ciphertext attacks allow conversion of a BasicHCBE scheme to aFullHCBE scheme that is chosen-ciphertext secure in the random oraclemodel. FIG. 9 illustrates a FullHIDE based scheme that ischosen-ciphertext secure.

FIG. 9 shows a flow diagram illustrating a method of encoding anddecoding a digital message M communicated between a sender y and arecipient z according to another presently preferred embodiment of theinvention. The Root Setup, Lower-level Setup, Extraction andCertification algorithms are the same for this embodiment of theinvention as for the embodiment described with reference to FIG. 7,except that the Root Setup algorithm of this embodiment requires twoadditional functions. Accordingly, the flow diagram of FIG. 9 beginswith the selection of the additional functions (blocks 915 a and 915 b)and continues with the Encryption and Decryption algorithms (blocks 930a through 932 d).

The Root Setup algorithm is completed by selecting a third function H₃(block 915 a) and a fourth function H₄ (block 915 b). The third functionH₃ preferably is capable of generating an integer of the cyclic group

/q

from two strings of binary digits. The fourth function H₄ preferably iscapable of generating one binary string from another binary string.

The Encryption algorithm begins with block 930 a, which shows theselection of a random binary string σ. The random binary string σ isthen used to generate a random integer r=H₃(σ, M), as shown in block 930b. W is a symmetric encryption of the actual message M preferablygenerated using a symmetric encryption algorithm E, and using H₄(σ) asthe encryption key. Accordingly, W=E_(H) ₄ _((σ))(M). In block 930 c,the ciphertext C=[U₀, U₂, . . . , U_(n+1), V, W] is generated. Theciphertext C includes elements U₀=rP₀, and U_(i)=rP_(zi) for 2≦i≦n+1,which relate to the recipient's public key and the location of therecipient in the hierarchy. The second part of the ciphertext C is therandom binary string σ in encrypted form, V=σ

H₂(g^(r)), wherein g=ê(Q₀, P_(z1)). The element g preferably is a memberof the second cyclic group

₂. The third part of the ciphertext C is the actual message in encryptedform, as described above.

The Decryption algorithm begins with block 932 a, which shows therecovery of the random binary string σ. The random binary string σ isrecovered using the formula

$\sigma = {V \oplus {{H_{2}( \frac{\hat{e}( {U_{0},S_{z{({n + 1})}}} )}{\prod\limits_{i = 2}^{n + 1}\;{\hat{e}( {Q_{i - 1},U_{i}} )}} )}.}}$The message M is then recovered from the ciphertext C (block 932 b)using the formula M=E_(H) ₄ _((σ)) ⁻¹(W). The ciphertext optionally maybe checked for internal consistency. For instance, an experimentalrandom integer r′=H₃(σ, M) may be generated, as shown in block 932 c.The experimental random integer r′ then may be used in block 932 d toconfirm that U₀=r′P₀ and U_(i)=r′P_(zi) for 2≦i≦n+1. If so, then theciphertext C is considered authentic.

The concept of dual-HCBE described with reference to FIGS. 5 and 6 maybe applied to BasicHCBE and FullHCBE schemes. When both the sender andrecipient are within the hierarchical structure, as shown in FIG. 6,dual-HCBE allows them to increase the efficiency and security of theirencrypted communications. The application of dual-HCBE to BasicHCBE andFullHCBE schemes requires the determination of additional information,most of which is determined via the Lower-level Setup algorithmdescribed above. For instance, elements P_(yi), lower-level keygeneration secrets s_(yi), lower-level secret elements S_(yi), andlower-level key generation parameters Q_(yi) must be determined for thesender's m ancestral lower-level authorizers. Note, however, that forthe lower-level authorizers that are common ancestors to both the sendery and the recipient z, these parameters preferably will be the same forpurposes of analyzing both the sender y and the recipient z (i.e., forall i≦l: P_(yi)=P_(zi), s_(yi)=s_(zi), S_(yi)=S_(zi), andQ_(yi)=Q_(yi)). Dual-HCBE also requires determination of a sender publicelement P_(y(m+1)) and a sender secret element S_(y(m+1)) for thesender, using the same methods for which these parameters are determinedfor the recipient as described above.

Given these additional parameters, a message M may be encoded togenerate a ciphertext C according the principles of dual-HCBE by usingthe lower-level key generation parameters Q_(yi) for i≧l and the sendersecret element S_(y(m+1)), but not using the lower-level key generationparameters Q_(yi) for i<l. Similarly, the ciphertext C may be decoded torecover the message M using the lower-level key generation parametersQ_(zi) for i≧l and the recipient secret element S_(z(n+1)), but notusing the lower-level key generation parameters Q_(zi) for i<l.

For instance, in a BasicHCBE scheme (FIGS. 7 and 8), application ofdual-HCBE changes the encoding of the message M to generate a ciphertextC=[U₀, U_(l+1), . . . U_(n+1), V], wherein U₀=rP, and U_(i)=rP_(zi) for2≦i≦n+1, wherein V=M

H₂(g_(yl) ^(r)), and wherein

$g_{yl} = {\frac{\hat{e}( {P_{0},S_{y{({m + 1})}}} )}{\prod\limits_{i = {l + 1}}^{m + 1}\;{\hat{e}( {Q_{y{({i - 1})}},P_{yi}} )}}.}$The U_(i) factors are calculated in the same way as before, but fewer ofthem are necessary. However, dual-BasicHCBE does require the sender y touse more key generation parameters Q_(yi) to generate g_(yl) than arenecessary to generate g as describe above. This is because theEncryption algorithm incorporates the sender's identity.

The increase in efficiency of the Decryption algorithm is more dramatic.The message M is recovered using

$M = {V \oplus {{H_{2}( \frac{\hat{e}( {U_{0},S_{z{({n + 1})}}} )}{\prod\limits_{i = {l + 1}}^{n + 1}\;{\hat{e}( {Q_{z{({i - 1})}},U_{zi}} )}} )}.}}$Again, fewer U_(i) parameters are necessary. Similarly, the recipientrequires fewer key generation parameters Q_(zi) for dual-HCBE than wouldotherwise be necessary.

FullHCBE also may be modified to create a dual-FullHCBE scheme.Generation of the ciphertext C in the Encryption algorithm is modifiedsuch that C=[U₀, U,_(l+1), . . . , U_(n+1), V, W], wherein U₀=rP, andU_(i)=rP_(zi) for l+1≦i≦n+1. The W and r parameters are still generatedthe same way, W=E_(H) ₄ _((σ))(M), but the g_(yl) parameter in V=σ

H₂ (g_(yl) ^(r)) is generated using

$g_{yl} = {\frac{\hat{e}( {P_{0},S_{y{({m + 1})}}} )}{\prod\limits_{i = {l + 1}}^{m + 1}\;{\hat{e}( {Q_{y{({i - 1})}},P_{yi}} )}}.}$

The Decryption algorithm also is modified in a dual-FullHCBE scheme. Therandom binary string σ is recovered using

$\sigma = {V \oplus {{H_{2}( \frac{\hat{e}( {U_{0},S_{z{({n + 1})}}} )}{\prod\limits_{i = {l + 1}}^{n + 1}\;{\hat{e}( {Q_{z{({i - 1})}},U_{zi}} )}} )}.}}$Otherwise, recovery of the message M does not change.Aggregate Signature CBE

In another embodiment of the present invention, a scheme may be used tocompress signatures on any type of information in an authorization chainto a single point, i.e. given n signatures on n distinct messages from ndistinct users, it is possible to aggregate all these signatures into asingle short signature. D. Boneh, C. Gentry and B. Lynn and H. Shacham,Aggregate and Verifiably Encrypted Signatures from Bilinear Maps, eprintarchive, 2002, available at h-t-t-p://eprint.iacr.org/2002/175/ describea bandwidth-efficient aggregate signature scheme in which multiplesignatures by multiple signers on multiple documents may be compactlyrepresented as a single point on an elliptic curve.

In such an aggregate-signature-based CBE protocol, the recipient canonly decrypt an encrypted message if it possesses the signaturesgenerated by the authorizers, in addition to the recipient's privatekey, SK_(B). Here, the public key of each required signer (an element of

₁) is readily available to users of the cryptosystem, as are a point Pon the elliptic curve and a function H that maps messages to points onthe elliptic curve.

In one embodiment of aggregate signature CBE, the ith signer choosess_(i) as its private key and computes s_(i)P as its public key. The ithsigner then signs a document M_(i) by computing P_(Mi)=H(M_(i)) andsends its signature S_(i)=s_(i)P_(Mi) to the recipient. Any entity,including the verifier, can verify that S_(i) is a legitimate signatureby the ith signer by checking that ê(P,S_(i))=ê(s_(i)P,P_(Mi)). Anyentity can also aggregate the signatures by summing them up. Any entitythat knows the aggregate signature S, the public keys of the signers,and the respective documents being signed can verify that the aggregatesignature is legitimate by checking that ê(P,S)=

^(n) _(i=1)ê(s_(i)P,P_(Mi)).

The message sender encrypts its message so that the message recipientneeds the recipient private key and a specified aggregate signature inorder to decrypt. Using the message recipient's public key, the publickeys of the specified signers, and the specified documents to be signed,the message sender encrypts a message M by setting the ciphertext to be:

-   -   C=[rP, M        H2(g^(r))], where g=ê(s_(B)P,P′_(B))        ^(n) _(i=1)ê(s_(i)P,P_(Mi)) and where P′_(B)=H1(Inf_(rec)).

The message recipient computes g^(r)=ê(rP,s_(B)P′_(B))ê(rP,S), whichallows recovery of the message M.

The document M_(i) may comprise any type of digital information and oneof more of the authorizers may sign different documents. In oneembodiment of the invention, a document M_(i) includes the validityperiod for the recipient's public key and can include other identifyinginformation, including the recipient's public key. In this embodiment,the recipient can decrypt only if the aggregate signature includes theith signer's signature on M_(i) attesting that the recipient's publickey is valid for period i.

In another embodiment of the invention, the authorizers form anaggregate signature hierarchy including at least a root authorizer and nlower-level authorizers in the hierarchy between the root authorizersand the entity, wherein n≧1. For example, the recipient may be at levelt in the hierarchy with authorizers above having public keys s_(K)P for0≦k≦t−1. Each authorizer certifies the public key of the authorizerbelow it, producing s_(K)P_(k+1) for 0≦k≦t−2, whereP_(k+1)=H₁(CA_(k+1)name, s_(K+1)P). Here, CA_(k+1)name is theidentifying information for the authorizer at level k+1. The authorizerat level t−1 certifies the recipient, producing s_(t−1)P_(B), whereP_(B)=H₁(Recipient_(name), s_(b)P, i). Here, recipient_(name) is therecipient's identifying information, s_(B)P is the recipient's publickey, and i is a parameter determining the validity period of therecipient's public key.

To encrypt M, the sender chooses a random r∈

/q

and creates ciphertext C=[rs_(B)P, M

H₂(g^(r))], where g=Π^(t−1) _(i=1)ê(P_(K), s_(K−1)P) ê(P_(B), s_(t)P).To decrypt, the recipient is assumed to have possession of the aggregateof the t certificates S_(B)=s_(t−1)P_(B)+Σ_(k=1) ^(t−1)S_(k−1)P_(k). Therecipient computes s_(B) ⁻¹S_(B) and then decrypts M=V

H₂(ê(rs_(B)P,s_(B) ⁻¹S_(B))).

Here, encryption involves t pairing computations. However, decryptiontime and the ciphertext length are the same as Boneh-Franklin. Thismethod offers advantages over the hierarchical schemes described abovethere the length of the ciphertext is basically proportional to t.

As in the schemes mentioned above, aggregate signature CBE may be madechosen-ciphertext secure in the random oracle model using theFujisaki-Okamoto transform.

CBE Using General Pairing-Based Signatures

The description above discusses different pairing-based embodiments ofCBE in which the recipient decryption key is a pairing-based signature.For example, in the simplest version of pairing-based CBE, the recipientdecryption key is a single element of

₁ that is a single authorizer's signature on a single document. In thepairing-based embodiments of HCBE and dual-HCBE, the recipientdecryption key is a hierarchical identity-based signature on a singledocument consisting of a plurality of elements of

₁. In the pairing-based embodiment of aggregate signature CBE, therecipient decryption key represents multiple signatures by multiplesigners on multiple documents that may be aggregated into a singleelement of

₁. In general, the verification algorithm in these signature schemesworks by confirming that a product of pairings of public key points andmessage points—e.g., s_(i)P and P_(Mi) for aggregate signatures—equals aproduct of pairings of signature points and dummy points—e.g.,s_(i)P_(Mi) and P for aggregate signatures. In another embodiment of thepresent invention, any pairing-based signature scheme may be used toconstruct a pairing-based CBE scheme, where a pairing-based signaturescheme is defined herein to be one in which the verification algorithmworks by confirming that a product of pairings of the public key pointsand message points equals a product of pairings of the signature pointsand dummy points.

For example, suppose that the verification algorithm confirms that Π^(n)_(i=1)ê(Q_(i), P_(Mi))=Π^(n) _(i=1)(S_(i), D_(i)), where the Q's arepublic key points, the P's are message points, the S's are signaturepoints, and the D's are decryption points, not necessarily distinct. Ifthe signature scheme is secure, a secure pairing-based CBE scheme may beconstructed. The sender chooses a random r∈

/q

and creates ciphertext C=[rD₀, rD₁, . . . , rD_(n), M

H₂(g^(r))], where g=e(s_(B)D₀,P′_(B))Π^(n) _(i=1)(Q_(i), P_(Mi)). If themessage recipient possesses all of the signature points—i.e., all of thenecessary authorizations, it may compute g^(r)=e(rD₀,s_(B)P′_(B))Π^(n)_(i=1)(S_(i), rD_(i)), and hence M. As previously, the scheme can bemade chosen-ciphertext secure in the random oracle model using theFujisaki-Okamoto transform.

High-Granularity CBE

Another embodiment of the invention combines a CBE scheme with aforward-secure encryption scheme operated in reverse to produce ahigh-granularity CBE scheme.

In a conventional forward-secure encryption scheme, the lifetime of thesystem is divided into a number of time-periods, each defining a keyvalidity period. This period is equivalent to the validity period of theidentity-based decryption key in a CBE system. In the forward-securesystem, the private key changes during successive time periods in such away that, if the key is compromised, an attacker cannot decrypt messagessent to the recipient in previous time periods. However, if the sendercontinues to use the key after compromise, the attacker can decryptmessages sent in subsequent time periods. J. Katz, A Forward-SecurePublic-Key Encryption Scheme, eprint archive, 2002, available ath-t-t-p://eprint.iacr.org/2002/060/, the contents of which areincorporated by this reference, describes such a forward-secure scheme.The security of the Katz scheme is based on the bilinear Diffie-Hellmanassumption in the random oracle model and may be extended to achievechosen-ciphertext security.

In a high-granularity CBE scheme of the present invention, theauthorizer uses a forward-secure system operated in reverse to issue arecipient identity-based decryption key that can be used to decryptmessages encrypted using a time period parameter set at or before aspecific time but not messages encrypted with a time parameter set at alater time.

In a conventional CBE scheme, the authorizer must issue anidentity-based decryption key to each potential message recipient forevery time period used during encryption. If the authorizer is to beable to respond quickly to situations in which a key is compromised, thekey must be valid for only a short time period. For example, theauthorizer may be required to issue a key having a validity period ofone minute, requiring the authorizer to issue a new key to each userevery minute. Transmitting such a large number of keys for all usersrequires considerable resources.

In the high-granularity authorized decryption scheme, the forward-securescheme allows the recipient to request a key update only when arecipient wishes to initiate a session of reading encrypted messages. Ifthe recipient has only four message reading sessions per day—e.g., itlogs into its email accounts only once every few hours—only four keysare required, regardless of how many actual messages the messagerecipient decrypts. Each key will allow the recipient to decrypt allmessages encrypted using a time parameter set earlier than or at thetime it requests the key but not messages encrypted with a parameterindicating a later time. High-granularity CBE reduces transmission costsby reducing the number of identity-based decryption keys transmitted bythe authorizer. The scheme offers various tradeoffs compared to anonline scheme or a conventional high-granularity scheme.

In an online scheme, the authorizer collaborates with the recipient oneach message decryption. Thus, in comparing an online approach with ahigh-granularity CBE scheme, the most important metric is how manymessages a recipient expects to decrypt per session. A large number ofmessages per session favors the high-granularity CBE protocol, at leastin terms of minimizing the burden on the authorizer.

A conventional approach incorporating high time granularity requires themessage sender to perform an online check of the recipient's key statusbefore sending a message. Again, a high number of messages per sessionfavors the high-granularity CBE protocol over the conventional approach,since, in this case, the sender must perform an operation for eachmessage.

Where key updates occur at a high frequency, a high-granularity CBEscheme allows a recipient to download identity-based decryption keyinformation only when the recipient wishes to initiate a session ofreading messages. The downloaded information allows the decryption ofmessages encrypted using a time parameter up to the current time-period,but not messages encrypted using a time parameter for a latertime-period. Since the authorizer does not need to compute and transmita separate identity-based decryption key for each time-period that hastranspired, this decreases the workload on the authorizer compared to aconventional CBE scheme. The size of the download can be further reducedby downloading only the information required to compute keys for thetime-period since the previous download. (However, the fact that thatrecipients “pull” certificates from the authorizer, whereas theauthorizer may “push” certificates to recipients in a conventional CBEscheme, may introduce some additional workload on the authorizer.)

If desired, it is possible to combine a high-granularity CBE protocolwith a hierarchical certification scheme to avoid burdening a singleauthorizer with key-issuing responsibilities for an entire network.

FIG. 10 shows a diagram illustrating one embodiment of ahigh-granularity CBE scheme. Here, the lifetime of the scheme is dividedinto a number of time periods. For example, since there areapproximately 2¹¹ minutes in a day, an 11-bit binary string b₁. . . b₁₁may be assigned to each minute. Each binary string defines a time-periodidentification parameter representing the “identity” of a specific timeminute. If the system lifetime is longer than one day, each day forms aportion of the system lifetime. A time portion identifying parameterthat specifies the date (the “identity” of the day) may be specifiedseparately. Alternatively, the identity of the recipient may alsospecify the date.

FIG. 10 illustrates one embodiment of a high-granularity CBE protocol.In FIG. 10, the successive time-periods 901 are represented by the leafsof a binary tree of height t. Here, successive time-periods areassociated with the leaves of the tree, which are labeled with strings<i> of length t, i.e. time period i is associated with the leaf labeledby <i>.

Each node w 902 of the tree, including the leaf nodes are assigned asecret key sk_(w) by the authorizer. To decrypt a message encryptedusing PK during period i, only key ski_(<i>) is needed. In addition,given key sk_(w), it is possible to efficiently derive descendant keyssk_(w0) and sk_(w1) for descendant nodes w₀ 904 and w₁ 905 and thedescendants derived of these nodes. However, given PK and i, and withoutsk_(w) for all prefixes w of <i>, it is infeasible to derive s_(ki<i>)or to decrypt messages encrypted during time-periods up to including i.

For example, if the authorizer wishes to allow the recipient to decryptmessages during time periods 1-3 but not messages send during subsequenttime periods, the authorizer will give the recipient the keys associatedwith node w0 904 and w10 908. The recipient can generate the keysassociated with time-periods 1-2, i.e. w00 906 and w01 907, from key w0904 and has the key for time period 3, i.e. w10 908. However, therecipient cannot decrypt messages during time period 4 909 or subsequenttime periods.

In one embodiment of the invention, a pairing-based high-granularity CBEscheme includes four randomized algorithms: setup, key generation andcertification, encryption, and decryption.

During setup, the authorizer uses

, a BDH parameter generator, and a security parameter k to generategroups

₁ and

₂ of some prime order q and an admissible pairing ê:

₁×

₁→

G₂ as is described in the above CBE schemes. Again, the pairing isadmissible if it is bilinear, non-degenerate and computable.

The authorizer selects a key generation secret and establishes systemparameters by choosing an arbitrary generator P∈

₁, picking a random s_(c)∈

/q

, setting Q=s_(c)P, and choosing cryptographic functions H₁: {0,1}* →

₁ and H₂:

₂→{0,1}^(n) for some n. Here, the message space is

={0,1}^(n), the system parameters are params=(

₁,

₂, ê, P, Q, H₁, H₂), and the authorizer's master key generation secretis s_(c)∈

/q

.

In the key generation and certification algorithm, the authorizer thengenerates the recipient's identity-based decryption key. The key SK_(i)for time period i will consist of sk_(<i>) and {sk _(<i0 . . . ik−i0>)}for all 1≦k≦t such that i_(k)=1, i.e. the secret keys for all timeperiods up to and including time period i. Here, SK_(j) is computablefrom SK_(i) when j≦i.

When a user requests SK_(i) from the authorizer, the authorizer choosesrandom x∈Z/qZ. For w=<i> and for all w=i₀ . . . i_(k−1)0 with 1≦k≦t suchthat i_(k)=1, it computes S_(w)=s_(C)H₁(i₀, Inf_(z))+xH₁(w) and setssk_(w)={xP, S_(w)}. It sends these sk_(w) to the recipient.

In the encryption algorithm, the sender selects a random r and encryptsa message to form a ciphertext C by setting the ciphertext to:C=[rs _(B) P, rH ₁(j ₀ j ₁), . . . , rH1(j₀ . . . j _(t)), M

H2(g ^(r))],

where s_(B)P is the recipient's public key, j is a time period chosen bythe sender, and g=e(Q, H₁(i₀, Inf_(z))).

In the decryption algorithm, a recipient possessing SK_(i) for j≦i knowssk_(w) for some w that is a prefix of j—i.e., some w=j₀ . . . j_(k) forsome k≦t. Using this sk_(w), it decrypts C=[U₀, U₁, . . . , U_(t), V] bycomputing:g ^(r) =e(U ₀ , s _(B) ⁻¹ S _(w))/e(xP,U _(k)),and then M=V

H2(g ^(r)).Combining Certification Reconfirmation and CBE

The CBE schemes discussed require that the authorizer sign eachrecipient's decryption key individually. For example, if a system has250 million users and the time granularity is one day and each userreceives a decryption key for each time-period, the authorizer wouldhave to generate and transmit 250 million identity-based signatures perday.

A good PKI proposal must balance cryptographic and algorithmicconsiderations with real world technological limitations. In terms ofefficiency, two important factors are the amount of computationperformed by each type of entity (e.g. the authorizer) and thecommunication costs between the entities. Other embodiments of thepresent invention provide for computationally efficient techniques forthe authorizer to issue new decryption keys to users of the system.

A CBE scheme that amortizes public key operations over multiple usersoffers advantages in terms of efficiency. In a CBE scheme, thecertificates issued by the authorizer must also serve as decryption keysin a public-key encryption scheme. These decryption keys must becomputed using public key operations. However, by using efficient datastructures, like B-trees, the authorizer need not necessarily performO(N) public key operations per day, despite having N clients.

In one embodiment of the present invention, each client of theauthorizer is assigned a long-lived (e.g., one-year) certificate, whichthe authorizer periodically “reconfirms” (e.g., every day). Thelong-lived certificate may be generated in a number of ways. Forexample, it could be created using a scheme similar to that describedabove. In any case, if the message sender has the message recipient'slong-lived certificate, the sender can use CBE to protect against thepossibility that the recipient's public key has been revoked before itsintended date of expiration.

In cryptography, there is a broadcast encryption technique using theleafs of binary trees to represent the N users in a system. Here, auser's m=log N secret keys are the secret keys of the m nodes that arethe leaf's ancestors (including the leaf itself). FIG. 11 illustratessuch a system. Here, if user 4 is authorized to the broadcast, theauthorizer encrypts the session broadcast key with the secret key of oneof its m ancestors 1101, 1102, 1103 . . . 1104. If user 4 is notentitled to the broadcast, the m secret keys corresponding to nodes that“hang off” the path from the root to this leaf are used instead.

When R users are not entitled to the broadcast, the session broadcastkey is encrypted using R log(N/R) node keys, where these nodes form a“cover” of the N-R entitled users. FIG. 12 illustrates the concept of“cover”. Here, the keys associated with nodes 1201 provide cover forusers 1, 3, 4, 5, 6, 7, 8, i, and i+1 but not the other users.

One embodiment of a CBE scheme applies this technique. A unique binarystring is generated associating the recipient with a leaf node in aB-tree. Unique binary strings associated with each ancestor node of therecipient leaf node are also generated. In the present pairing-basedembodiment, the authorizer establishes some public way of associatingthe binary strings to points P_(node) on the relevant elliptic curve (orabelian variety).

These binary strings may be generated in a number of ways. For example,the authorizer may compute a node's binary string asfunction(stringparent, O) or function(stringparent, 1), depending onwhether the node is the left or right child of its parent.Alternatively, binary strings can be assigned to each recipient leafnode and the binary strings associated with ancestor generated using atleast the binary strings associated with the child nodes of these nodes.Each binary string can then be mapped to a point on an elliptic curve orabelian variety using a function. In one embodiment, the function may bea hash function.

The decryption key corresponding to a node's point P_(node), iss_(c)P_(node), where s_(c) is a master secret kept by the authorizer.The authorizer finds a cover of the users to be reconfirmed, and thenperiodically publishes the decryption keys corresponding to the nodes inthat cover. Every reconfirmed user can find some decryption keys_(c)P_(node), such that node is an ancestor of its leaf. Thisdecryption key may also be associated with a parameter establishing avalidity period for the decryption key. For example, P_(node) may dependon this parameter.

If the point P_(node) associated with the decryption key s_(c)P_(node)are known to the sender, the sender can encrypt a message to therecipient using the recipient's public key PK_(B) and an encryption keyforming a public key/private key pair with the decryption key.

However, since the sender may not know the cover used by the authorizer,the sender may not know which of the recipient's ancestor nodes thisdecryption key corresponds to. Thus, the sender generates m separateencryptions of the message.

The sender chooses a random r and computes rP. Next the sender encryptsthe ciphertext C=[rP, V₁, . . . , V_(m)], where V_(i)=M

H(ê(P,P_(i))^(rs) ^(c) ) and P_(i) is the identifying stringcorresponding to serial number b₁ . . . b_(i). Some part of theciphertext, e.g., M, is also encrypted with the recipient's public keyPK_(B). This could be done in a fashion similar to the schemes above,where the recipient uses its knowledge of s_(B) to compute s_(B)P′_(B),which it needs to decrypt.

An unrevoked recipient will have received some decryption key s_(c)P_(i)from the authorizer. The recipient uses this key, as well as therecipient's private key SK_(B), to decrypt one of the V_(i)'s.

If the decryption key is associated with a validity period parameter, amessage sender knowing the schedule by which the authorizer issues therecipient's decryption key can encrypt a message using the recipient'spublic key PK_(B) and an encryption key forming a public key/private keypair with the decryption key with a defined validity period. Therecipient may then only decrypt the message during this period.

In another embodiment of the present invention, only the root node pointP_(time) is computed as a function of the period validity parameter. Thelower-level nodes, i.e. those nodes between the root node and the leafrepresenting a recipient, are computed as functions of their positionsin the tree, e.g., P_(b1 . . . bi)=H(b₁ . . . b_(i)), and do not changewith time. The authorizer uses the technique described above to generatea decryption key for some ancestor of each leaf associated with arecipient that is not revoked. The decryption key for b₁ . . . b_(i) isof the form s_(C)P_(time)+x(P_(b1 . . . bi)), xP for some random x∈

/q

. Here, both s_(C) and x are secrets of the authorizer.

As compared to the previous embodiment, the authorizer's computationalload in computing these keys is not increased. However, the sender'sencryption time is reduced. To encrypt, the sender chooses a random rand computes rP. The sender then encrypts the ciphertext C:

-   -   C=[rP, rP_(b1), . . . , r(P_(b1)+ . . . +P_(b1 . . . bm)), V],        where V=M        H₂(ê(s_(C)P, P_(time))^(r))), ê(P, P_(time))∈        ₂. Again, some part of the ciphertext, e.g., M, is also        encrypted with the recipient's public key PK_(B).

An unrevoked recipient decrypts by dividing ê(rP, sP_(time)+x((P_(b1)+ .. . +P_(b1 . . . bi))) by ê(xP, r(P_(b1)+ . . . +P_(b1 . . . bi))). Therecipient also uses the recipient's private key SK_(B), to decrypt themessage. Here, the recipient has to perform one more pairing than theprevious embodiment. However, the sender performs fast pointmultiplications rather than slower pairing computations.

In yet another embodiment of the present invention, only the root nodepoint P_(time) is computed as a function of a certain specifiedtime-period, as above. However, in this embodiment, the amount of workperformed in a given time period by the authorizer depends only on thenumber of revocations that occurred during the previous time-period,rather than the total number of revoked recipients.

The lower-level nodes are again computed as functions of their positionsin the tree, e.g., P_(b1 . . . bi)=H(b₁ . . . b_(i)), and do not changeaccording to time. The authorizer generates a decryption key for someancestor of each unrevoked recipient.

If the authorizer performs decryption key updates at given timeintervals, e.g. every hour, the each hour has a point P_(hour)associated with it. The authorizer finds a cover of the recipients thathave not been revoked in the past hour, using the broadcast encryptiontechnique. This cover will consist of O(R log(N/R)) points, where R isthe number of recipients revoked in the past hour (not overall). Foreach node P_(i) in the cover, the authorizer issues a point of the formsP_(hour)+xP_(i) , along with the point xP. The authorizer chooses a newvalue of x for each hour. If a given recipient has not been revoked inthat hour, the recipient will have some ancestor P_(i) for which theauthorizer has issued a point. This point is the recipient'sreconfirmation certificate for that hour.

By adding its hourly reconfirmation certificates together, a recipientobtains an aggregated certificate of the form s(P_(hour1)+ . . .+P_(hourk))+x₁P₁+x₂P₂+ . . . +x_(m)P_(m), together with the points{x_(i),P}. This is the recipient's updated decryption key. At the end ofa chosen time interval, e.g. at the end of the day, the authorizerpublishes s(P_(day)−P₂₄− . . . −P₁). This allows all recipients thatwere certified throughout the day to compress the expression of the timecomponent of their private point. A recipient's complete private pointfrom day v hour y to day w hour z may look like:S _(recipient) =s(P _(v,y) + . . . +P _(v,24) +P _(v+1,1) + . . . +P_(w,z))+x _(i) P ₁ +x ₂ P ₂ + . . . +x _(m) P _(m).

The message sender can easily compute P_(Bper)=P_(v,y)+ . . . +P_(w,z),the point corresponding to the time period over which a recipient musthave been continuously reconfirmed. The sender encrypts a message to therecipient by first choosing a random r and then computing rP. The senderthen sets the ciphertext C to be:C=[rP, rP ₁ , . . . , rP _(m) , V], where V=M

H(ê(s _(c) P, P _(Bper))^(rs)).Again, some part of the ciphertext, e.g., M, is also encrypted withrecipient's public key PK_(B).

The recipient, if not revoked, decrypts to recover M via the formula:M=V

H(ê(rP, S _(recipient))/Π_(i=1) ^(m) ê(rPi, xiP))

The recipient also uses the recipient private key SK_(B) to perform somepart of the decryption

The advantages of the later embodiment may be illustrated by thefollowing example in which the authorizer has N=250,000,000 clients,performs updates every hour, and revokes R users per hour. In a systemof 250,000,000 users, 10% of which are revoked per year, about 2850users are revoked per hour. Since R log(N/R)˜46000, the authorizer mustgenerate about 13 reconfirmation certificates per second. This is quitereasonable on a single computer. However, the CA can have severalcomputers to allow the computation to be distributed. Signaturegeneration merely involves point multiplication on elliptic curves,which is fast ECC-type operation.

Distributing these certificates can be handled in a number of differentways. One option is to “push” certificates to the recipients theycertify. Potentially, multicast could make this very efficient, reducingthe authorizer's bandwidth needs to (46000 certs)*(320 bits percertification)/hour≈4 kbits/sec. If multicast is not used, pushingcertificates directly to all 250,000,000 users would require the CA tohave at least 22 tobit/sec connection, which, since it is a lower bound,may be infeasible. This figure might be reduced if clients “pull” theircertificates from the CA less than 24 times per day, but the bandwidthrequirements would still be substantial. If multiple (untrusted) serversare used, a (collective) 22 mbit/sec connection will allow the serversto push certificates to clients.

As an alternative, the clients could pull their certificates from theservers. It is not necessary for every server to store all of thereconfirmation certificates. Rather, the recipient can have a certainserver that it always retrieves its certificates from. In this case, theauthorizer-directory communication is not (4 kbits/sec)*(number ofservers); rather it remains 4 kbits/sec.

Regardless of the number of time periods that have passed from arecipient's initial certification to the present, the recipient's proofof certification remains compact: its private point Srecipient togetherwith its log N points {xiP}. At a small additional expense to thesender, the recipient can express each point using about 160 bits(instead of 320 bits). Thus, if N is 250,000,000, its aggregatedreconfirmation certificate is about 4.5 kbits.

Although the methods of the present invention all preferably require therecipient to have its own public key/private key pair so that only therecipient (or possibly a private key generator, if the recipient privatekey is identity-based) can decrypt, it will be understood by thoseskilled in the art that the methods can be weakened by not making such arequirement—i.e., by allowing the sender's message to be decrypted byany entity possessing the necessary signatures from the necessaryauthorizers even without a recipient private key.

Systems for Use with Certificate-Based Encryption Schemes

Various methods of sending a digital message between a sender and arecipient in a public-key encryption scheme have been described. Asystem for implementing these methods according to another embodiment ofthe present invention will now be described.

The system includes a number of terminals, each of which may beassociated with an entity that sends or receives messages according tothe methods described above. The system also includes one or moreauthorizers that certify that a message recipient has authority toreceive a message.

Each terminal includes a processor in bidirectional communication with amemory. The processor executes suitable program code for carrying outthe procedures described above. The processor also executes suitableprogram code for generating information to be transmitted to otherterminals. Suitable program code may be created according to methodsknown in the art. The memory stores the program code, as well asintermediate results and other information used during execution of themethods described above.

A communications network is provided over which the entities and theauthorizer(s) may communicate. The communications network may be ofvarious common forms, including, for instance, a LAN computer network, aWAN computer network, and/or a mobile telephone network provide suitablecommunication networks.

The invention has been described in detail with particular reference topreferred embodiments thereof and illustrative examples, but it will beunderstood that variations and modifications can be effected within thespirit and scope of the invention.

1. A method for operating a public-key encryption scheme which providesfor sending a digital message M between a sender and a recipient withparticipation of an authorizer, wherein the digital message is encryptedby the sender and decrypted by the recipient, the method comprisingencrypting, by at least one machine in a set of one or more machines,the digital message M using at least a recipient public key RPUB and arecipient encryption key RENC to create an encrypted digital message fordecryption with a recipient private key RPRIV and a recipient decryptionkey RDEC, wherein: the recipient public key RPUB and the recipientprivate key RPRIV form a public key/private key pair 1, wherein therecipient private key RPRIV is a secret of the recipient; the recipientdecryption key RDEC is generated by the authorizer using at least a keygeneration secret of the authorizer and the recipient encryption keyRENC, wherein the recipient encryption key RENC and the recipientdecryption key RDEC are a public key/private key pair 2; wherein therecipient encryption key RENC is generated from information comprisingthe identity of the recipient, the recipient public key RPUB, and aparameter defining a validity period for the recipient decryption keyRDEC.
 2. A system configured to perform the method of claim 1, thesystem comprising: at least one computer system comprising one or moreprocessors and memory, for acting as said authorizer; at least onecomputer system comprising one or more processors and memory, for actingas said sender; and at least one computer system comprising one or moreprocessors and memory, acting as said recipient.
 3. The method of claim1, wherein the recipient decryption key RDEC is generated by theauthorizer according to a schedule known to the sender.
 4. Anon-transitory computer-readable medium comprising a computer-readableprogram operable to cause a computer to perform the method of claim 3.5. A system configured to perform the method of claim 3, the systemcomprising: at least one computer system comprising one or moreprocessors and memory, for acting as said authorizer; at least onecomputer system comprising one or more processors and memory, for actingas said sender; and at least one computer system comprising one or moreprocessors and memory, acting as said recipient.
 6. The method of claim3, wherein the recipient encryption key RENC is generated using at leastinformation comprising the schedule.
 7. A non-transitorycomputer-readable medium comprising a computer-readable program operableto cause a computer to perform the method of claim
 6. 8. A systemconfigured to perform the method of claim 6, the system comprising: atleast one computer system comprising one or more processors and memory,for acting as said authorizer; at least one computer system comprisingone or more processors and memory, for acting as said sender; and atleast one computer system comprising one or more processors and memory,acting as said recipient.
 9. The method of claim 1, wherein therecipient private key RPRIV and the recipient public key RPUB aregenerated using at least one system parameter issued by the authorizer.10. The method of claim 1, wherein the recipient decryption key RDEC isgenerated by the authorizer to have a value S=s_(c)P_(B), wherein: s_(c)is the key generation secret of the authorizer; and P_(B) is therecipient encryption key RENC and is equal to H₁(Inf_(B)), whereinInf_(B) is an element of a first cyclic group

₁ of elements, wherein P_(B) is an element of a second cyclic group

₂ of elements, and H₁ is a predefined function (“first function H₁”),wherein the first and second cyclic groups

₁ and

₂ and the function H₁ are system parameters made available to thesender, and also available to the sender are system parameterscomprising: a generator P of the first cyclic group

₁; a key generation parameter Q=S_(C)P; a second function H₂ capable ofgenerating a second string of binary digits from an element of thesecond cyclic group

₂.
 11. The method of claim 10, wherein both the first group

₁ and the second group

₂ are of the same prime order q.
 12. The method of claim 11 wherein:s_(C) is an element of the cyclic group

/q

.
 13. The method of claim 10 wherein the first cyclic group

₁ is an additive group of points on a supersingular elliptic curve orabelian variety, and the second cyclic group

₂ is a multiplicative subgroup of a finite field.
 14. The method ofclaim 10 wherein the system parameters available to the sender furthercomprise a function ê which is a bilinear, non-degenerate, andefficiently computable pairing which maps

₁×

₁ into

₂.
 15. A non-transitory computer-readable medium comprising acomputer-readable program operable to cause a computer to perform themethod of claim
 10. 16. A system configured to perform the method ofclaim 10, the system comprising: at least one computer system comprisingone or more processors and memory, for acting as said authorizer; atleast one computer system comprising one or more processors and memory,for acting as said sender; and at least one computer system comprisingone or more processors and memory, acting as said recipient.
 17. Themethod of claim 10 wherein the method further comprises the authorizerselecting, by at least one machine in the set of the one or moremachines, said key generation secret and generating, by at least onemachine in the set of the one or more machines, the recipient decryptionkey RDEC and sending, by at least one machine in the set of the one ormore machines, the recipient decryption key RDEC to the recipient. 18.The method of claim 1, wherein the recipient encryption key RENC isgenerated from a document and the recipient decryption key RDEC is theauthorizer's signature on the document.
 19. A non-transitorycomputer-readable medium comprising a computer-readable program operableto cause a computer to perform the method of claim
 18. 20. A systemconfigured to perform the method of claim 18, the system comprising: atleast one computer system comprising one or more processors and memory,for acting as said authorizer; at least one computer system comprisingone or more processors and memory, for acting as said sender; and atleast one computer system comprising one or more processors and memory,acting as said recipient.
 21. The method of claim 1 wherein the methodfurther comprises the recipient performing, by at least one machine inthe set of the one or more machines, operations of: generating therecipient public key RPUB and the recipient private key RPRIV;decrypting the encrypted digital message using at least the recipientprivate key RPRIV and the recipient decryption key RDEC.
 22. The methodof claim 1 wherein the method further comprises the authorizerselecting, by at least one machine in the set of the one or moremachines, said key generation secret and generating the recipientdecryption key RDEC and sending the recipient decryption key to therecipient.
 23. The method of claim 22 wherein the method furthercomprises the recipient performing, by at least one machine in the setof the one or more machines, operations of: generating the recipientpublic key RPUB and the recipient private key RPRIV; decrypting theencrypted digital message using at least the recipient private key RPRIVand the recipient decryption key RDEC.
 24. A system configured toperform the method of claim 23, the system comprising: at least onecomputer system comprising one or more processors and memory, for actingas said authorizer; at least one computer system comprising one or moreprocessors and memory, for acting as said sender; and at least onecomputer system comprising one or more processors and memory, acting assaid recipient.
 25. The method of claim 1 further comprising generating,by at least one machine in the set of the one or more machines, therecipient encryption key RENC by the authorizer and/or the recipientand/or the sender.
 26. A non-transitory computer-readable mediumcomprising a computer-readable computer program operable to cause acomputer to perform the method of claim
 1. 27. The method of claim 1wherein the recipient private key RPRIV is generated by the recipientand is unknown to the authorizer.
 28. A method for operating apublic-key encryption scheme which provides for sending a digitalmessage between a sender and a recipient with participation of aplurality of authorizers, the plurality of authorizers including a rootauthorizer and n lower-level authorizers in a hierarchy between the rootauthorizer and the recipient, wherein n≧1, the method comprisingencrypting, by at least one machine in a set of one or more machines,the digital message using a recipient public key RPUB and a recipientencryption key RENC to create an encrypted digital message fordecryption with a recipient private key RPRIV and a recipient decryptionkey RDEC, wherein: the recipient encryption key RENC and the recipientdecryption key RDEC are a public key/private key pair 1; the recipientpublic key RPUB and the recipient private key RPRIV form a publickey/private key pair 2, wherein the recipient private key RPRIV is asecret of the recipient; the recipient encryption key RENC is generatedusing identity information of at least one of the recipient's ancestors;the recipient decryption key RDEC is generated by one of the authorizerssuch that the recipient decryption key RDEC is related to the recipientencryption key RENC, a root key generation secret and an associated rootkey generation parameter, wherein the root key generation parameter isgenerated based on the root key generation secret, and the root keygeneration secret is a secret of the root authorizer; wherein therecipient encryption key RENC is generated from information comprisingthe identity of the recipient, the recipient public key RPUB, and aparameter defining a validity period for the recipient decryption keyRDEC.
 29. The method of claim 28, wherein the recipient decryption keyRDEC is generated according to a schedule known to the sender.
 30. Anon-transitory computer-readable medium comprising a computer-readableprogram operable to cause a computer to perform the method of claim 29.31. A system configured to perform the method of claim 29, the systemcomprising: at least one computer system comprising one or moreprocessors and memory, for acting as said authorizer; at least onecomputer system comprising one or more processors and memory, for actingas said sender; and a plurality of computer systems each comprising oneor more processors and memory, acting as said authorizers.
 32. Themethod of claim 28, wherein the recipient private key RPRIV and therecipient public key RPUB are generated using system parameters issuedby one or more of the authorizers.
 33. The method of claim 28, whereinthe recipient decryption key RDEC is related to the root key generationsecret and the associated root key generation parameter.
 34. The methodof claim 33 wherein the method further comprises generating, by at leastone machine in the set of the one or more machines, the recipientdecryption key RDEC by one of the authorizers.
 35. The method of claim28, wherein the plurality of authorizers further includes at least inlower-level authorizers in the hierarchy between the root authorizer andthe sender, wherein in m≧1, and wherein l of the m authorizers in thehierarchy are common ancestors to both the sender and the recipient,wherein authorizer_(l) is the lowest common ancestor authorizer betweenthe sender and the recipient, and wherein l≧1, and wherein: alower-level key generation secret is selected for each of the mlower-level authorizers in the hierarchy between the root authorizer andthe sender; and a sender decryption key SDEC is generated such that thesender decryption key SDEC is related to at least the root keygeneration secret and one or more of the m lower-level key generationsecrets associated with the in lower-level authorizers in the hierarchybetween the root authorizer and the sender; wherein the message isencrypted using at least the sender decryption key SDEC and one or moreof the lower-level key generation parameters associated with the (m−l+1)authorizers between the root authorizer and the sender that are at orbelow the level of the lowest common ancestor authorizer_(l), but notusing any of the lower-level key generation parameters that areassociated with the (l−1) authorizers above the lowest common ancestorauthorizer_(l); and wherein the encrypted digital message is decryptableusing at least the recipient decryption key RDEC and one or more of thelower-level key generation parameters associated with the (n−l+1)authorizers between the root authorizer and the sender that are at orbelow the level of the lowest common ancestor authorizer_(l), but notusing any of the lower-level key generation parameters that areassociated with the (l−1) authorizers that above the lowest commonancestor authorizer_(l).
 36. A non-transitory computer-readable mediumcomprising a computer-readable program operable to cause a computer toperform the method of claim
 35. 37. A system configured to perform themethod of claim 35, the system comprising: at least one computer systemcomprising one or more processors and memory, for acting as saidauthorizer; at least one computer system comprising one or moreprocessors and memory, for acting as said sender; and a plurality ofcomputer systems each comprising one or more processors and memory,acting as said authorizers.
 38. The method of claim 28 wherein themethod further comprises the root authorizer performing, by at least onemachine in the set of the one or more machines, operations of: selectingthe root key generation secret that is a secret of the root authorizer;and generating the root key generation parameter based on the root keygeneration secret.
 39. The method of claim 28 wherein the method furthercomprises generating, by at least one machine in the set of the one ormore machines, the recipient decryption key RDEC by one of theauthorizers.
 40. The method of claim 38 wherein further comprising therecipient performing, by at least one machine in the set of the one ormore machines, operations of: generating the recipient public key RPUBand the recipient private key RPRIV; and decrypting the encrypteddigital message to recover the digital message using at least therecipient private key RPRIV and the recipient decryption key RDEC. 41.The method of claim 28 further comprising generating, by at least onemachine in the set of the one or more machines, the recipient encryptionkey RENC.
 42. A non-transitory computer-readable medium comprising acomputer-readable computer program operable to cause a computer toperform the method of claim
 28. 43. A method for operating a public-keyencryption scheme which provides for sending a digital message between asender and a recipient with participation of a plurality of authorizers,the plurality of authorizers including a root authorizer and nlower-level authorizers in a hierarchy between the root authorizer andthe recipient, wherein n≧1, the method comprising encrypting, by atleast one machine in a set of one or more machines, the digital messageusing a recipient public key RPUB and a recipient encryption key RENC tocreate an encrypted digital message for decryption with a recipientprivate key RPRIV and a recipient decryption key RDEC, wherein: therecipient encryption key RENC and the recipient decryption key RDEC area public key/private key pair 1; the recipient public key RPUB and therecipient private key RPRIV form a public key/private key pair 2,wherein the recipient private key RPRIV is a secret of the recipient;the recipient encryption key RENC is generated using identityinformation of at least one of the recipient's ancestors; the recipientdecryption key RDEC is generated such that the recipient decryption keyRDEC is related to the recipient encryption key RENC, a root keygeneration secret and an associated root key generation parameter,wherein the root key generation parameter is generated based on the rootkey generation secret, and the root key generation secret is a secret ofthe root authorizer; wherein the method further comprises the recipientperforming, by at least one machine in the set of the one or moremachines, operations of: generating the recipient public key RPUB andthe recipient private key RPRIV; and decrypting the encrypted digitalmessage to recover the digital message using at least the recipientprivate key RPRIV and the recipient decryption key RDEC; wherein therecipient encryption key RENC is generated from information comprisingthe identity of the recipient, the recipient public key RPUB, and aparameter defining a validity period for the recipient decryption keyRDEC.
 44. A method for operating a public-key encryption scheme whichprovides for sending a digital message M between a sender and arecipient with participation of an authorizer, wherein the digitalmessage M is encrypted by the sender using at least a recipient publickey RPUB and a recipient encryption key RENC to create an encrypteddigital message and is decrypted by the recipient, the method comprisingdecrypting, by at least one machine in a set of one or more machines,the encrypted digital message using at least a recipient private keyRPRIV and a recipient decryption key RDEC, wherein: the recipient publickey RPUB and the recipient private key RPRIV form a public key/privatekey pair 1, wherein the recipient private key RPRIV is a secret of therecipient; the recipient decryption key RDEC is generated by theauthorizer using at least a key generation secret of the authorizer andthe recipient encryption key RENC, wherein the recipient encryption keyRENC and the recipient decryption key RDEC are a public key/private keypair 2; wherein the recipient encryption key RENC is generated frominformation comprising the identity of the recipient, the recipientpublic key RPUB, and a parameter defining a validity period for therecipient decryption key RDEC.
 45. The method of claim 44, wherein therecipient decryption key RDEC is generated by the authorizer accordingto a schedule known to the sender.
 46. A non-transitorycomputer-readable medium comprising a computer-readable program operableto cause a computer to perform the method of claim
 45. 47. A systemconfigured to perform the method of claim 45, the system comprising: atleast one computer system comprising one or more processors and memory,for acting as said authorizer; at least one computer system comprisingone or more processors and memory, for acting as said sender; and aplurality of computer systems each comprising one or more processors andmemory, acting as said authorizers.
 48. The method of claim 45, whereinthe recipient encryption key RENC is generated using at leastinformation comprising the schedule.
 49. A non-transitorycomputer-readable medium comprising a computer-readable program operableto cause a computer to perform the method of claim
 48. 50. A systemconfigured to perform the method of claim 48, the system comprising: atleast one computer system comprising one or more processors and memory,for acting as said authorizer; at least one computer system comprisingone or more processors and memory, for acting as said sender; and aplurality of computer systems each comprising one or more processors andmemory, acting as said authorizers.
 51. The method of claim 44, whereinthe recipient private key RPRIV and the recipient public key RPUB aregenerated using at least one system parameter issued by the authorizer.52. The method of claim 44, wherein the recipient decryption key RDEC isgenerated by the authorizer to have a value S=s_(c)P_(B), wherein: s_(c)is the key generation secret of the authorizer; and P_(B) is therecipient encryption key RENC and is equal to H₁(Inf_(B)), whereinInf_(B) is an element of a first cyclic group

₁ of elements, wherein P_(B) is an element of a second cyclic group

₂ of elements, and H₁ is a predefined function (“first function H₁”),wherein the first and second cyclic groups

₁ and

₂ and the function H₁ are system parameters made available to thesender, and also available to the sender are system parameterscomprising: a generator P of the first cyclic group

₁; a key generation parameter Q=s_(C)P; a second function H₂ capable ofgenerating a second string of binary digits from an element of thesecond cyclic group

₂.
 53. A non-transitory computer-readable medium comprising acomputer-readable program operable to cause a computer to perform themethod of claim
 52. 54. A system configured to perform the method ofclaim 52, the system comprising: at least one computer system comprisingone or more processors and memory, for acting as said authorizer; atleast one computer system comprising one or more processors and memory,for acting as said sender; and a plurality of computer systems eachcomprising one or more processors and memory, acting as saidauthorizers.
 55. The method of claim 52, wherein both the first group

₁ and the second group

₂ are of the same prime order q.
 56. The method of claim 52 wherein thefirst cyclic group

₁ is an additive group of points on a supersingular elliptic curve orabelian variety, and the second cyclic group

₂ is a multiplicative subgroup of a finite field.
 57. The method ofclaim 56 wherein: s_(C) is an element of the cyclic group

/q

.
 58. The method of claim 52 wherein the system parameters available tothe sender further comprise a function ê which is a bilinear,non-degenerate, and efficiently computable pairing which maps

₁×

₁ into

₂.
 59. The method of claim 44, wherein the recipient encryption key RENCis generated from a document and the recipient decryption key RDEC isthe authorizer's signature on the document.
 60. A non-transitorycomputer-readable medium comprising a computer-readable program operableto cause a computer to perform the method of claim
 59. 61. A systemconfigured to perform the method of claim 59, the system comprising: atleast one computer system comprising one or more processors and memory,for acting as said authorizer; at least one computer system comprisingone or more processors and memory, for acting as said sender; and aplurality of computer systems each comprising one or more processors andmemory, acting as said authorizers.
 62. The method of claim 44 furthercomprising the authorizer selecting, by at least one machine in the setof the one or more machines, said key generation secret and generating,by at least one machine in the set of the one or more machines, therecipient decryption key RDEC and sending, by at least one machine inthe set of the one or more machines, the recipient decryption key RDECto the recipient.
 63. A non-transitory computer-readable mediumcomprising a computer-readable computer program operable to cause acomputer to perform the method of claim
 44. 64. The method of claim 44wherein the recipient private key RPRIV is generated by the recipientand is unknown to the authorizer.
 65. A method for operating apublic-key encryption scheme which provides for sending a digitalmessage M between a sender and a recipient with participation of anauthorizer, wherein the digital message is encrypted by the sender usingat least a recipient public key RPUB and a recipient encryption keyRENC, wherein the recipient public key RPUB and a recipient private keyRPRIV form a recipient public key/recipient private key pair, whereinthe recipient private key RPRIV is a secret of the recipient, and thedigital message is decrypted by the recipient using at least therecipient private key RPRIV and a recipient decryption key RDEC, themethod comprising the authorizer performing, by at least one machine ina set of one or more machines, operations of: selecting a key generationsecret that is a secret of the authorizer; generating the recipientdecryption key RDEC using at least the key generation secret of theauthorizer and the recipient encryption key RENC, wherein the recipientencryption key RENC and the recipient decryption key RDEC are a publickey/private key pair; sending the recipient decryption key RDEC to therecipient; wherein the recipient encryption key RENC is generated frominformation comprising the identity of the recipient, the recipientpublic key RPUB, and a parameter defining a validity period for therecipient decryption key RDEC.
 66. The method of claim 65, wherein therecipient decryption key RDEC is generated by the authorizer accordingto a schedule known to the sender.
 67. A non-transitorycomputer-readable medium comprising a computer-readable program operableto cause a computer to perform the method of claim
 66. 68. A systemconfigured to perform the method of claim 66, the system comprising: atleast one computer system comprising one or more processors and memory,for acting as said authorizer; at least one computer system comprisingone or more processors and memory, for acting as said sender; and atleast one computer system comprising one or more processors and memory,acting as said recipient.
 69. The method of claim 66, wherein therecipient encryption key RENC is generated using at least informationcomprising the schedule.
 70. A non-transitory computer-readable mediumcomprising a computer-readable program operable to cause a computer toperform the method of claim
 69. 71. A system configured to perform themethod of claim 69, the system comprising: at least one computer systemcomprising one or more processors and memory, for acting as saidauthorizer; at least one computer system comprising one or moreprocessors and memory, for acting as said sender; and at least onecomputer system comprising one or more processors and memory, acting assaid recipient.
 72. The method of claim 65, wherein the recipientdecryption key RDEC is generated by the authorizer to have a valueS=s_(c)P_(B), wherein: s_(c) is the key generation secret of theauthorizer; and P_(B) is the recipient encryption key RENC and is equalto H₁(Inf_(B)), wherein Inf_(B) is an element of a first cyclic group

₁ of elements, wherein P_(B) is an element of a second cyclic group

₂ of elements, and H₁ is a predefined function (“first function H₁”),wherein the first and second cyclic groups

₁ and

₂ and the function H₁ are system parameters made available to thesender, and also available to the sender are system parameterscomprising: a generator P of the first cyclic group

₁; a key generation parameter Q=s_(C)P; a second function H₂ capable ofgenerating a second string of binary digits from an element of thesecond cyclic group

₂.
 73. The method of claim 72, wherein both the first group

₁ and the second group

₂ are of the same prime order q.
 74. The method of claim 73 wherein:s_(c) is an element of the cyclic group

/q

.
 75. The method of claim 72 wherein the first cyclic group

₁ is an additive group of points on a supersingular elliptic curve orabelian variety, and the second cyclic group

₂ is a multiplicative subgroup of a finite field.
 76. The method ofclaim 72 wherein the system parameters available to the sender furthercomprise a function ê which is a bilinear, non-degenerate, andefficiently computable pairing which maps

₁×

₁ into

₂.
 77. A non-transitory computer-readable medium comprising acomputer-readable program operable to cause a computer to perform themethod of claim
 72. 78. A system configured to perform the method ofclaim 72, the system comprising: at least one computer system comprisingone or more processors and memory, for acting as said authorizer; atleast one computer system comprising one or more processors and memory,for acting as said sender; and at least one computer system comprisingone or more processors and memory, acting as said recipient.
 79. Themethod of claim 65, wherein the recipient encryption key RENC isgenerated from a document and the recipient decryption key RDEC is theauthorizer's signature on the document.
 80. A non-transitorycomputer-readable medium comprising a computer-readable program operableto cause a computer to perform the method of claim
 79. 81. A systemconfigured to perform the method of claim 79, the system comprising: atleast one computer system comprising one or more processors and memory,for acting as said authorizer; at least one computer system comprisingone or more processors and memory, for acting as said sender; and atleast one computer system comprising one or more processors and memory,acting as said recipient.
 82. A non-transitory computer-readable mediumcomprising a computer-readable computer program operable to cause acomputer to perform the method of claim
 65. 83. The method of claim 65wherein the recipient private key RPRIV is unknown to the authorizer.84. A method for operating a public-key encryption scheme which providesfor sending a digital message between a sender and a recipient withparticipation of a plurality of authorizers, the plurality ofauthorizers including a root authorizer and n lower-level authorizers ina hierarchy between the root authorizer and the recipient, wherein n≧1,wherein the digital message is encrypted by the sender using a recipientpublic key RPUB and a recipient encryption key RENC to create anencrypted digital message for decryption by the recipient using arecipient private key RPRIV and a recipient decryption key RDEC, themethod comprising performing, by at least one machine in a set of one ormore machines, operations of: generating the recipient public key RPUBand the recipient private key RPRIV which are a public key/private keypair 1, wherein the recipient private key RPRIV is a secret of therecipient; obtaining an encrypted digital message formed by encryptionof the digital message with the recipient public key RPUB and therecipient encryption key RENC, wherein the recipient encryption key RENCand the recipient decryption key RDEC are a public key/ private key pair2; and decrypting the encrypted digital message to recover the digitalmessage using at least the recipient private key RPRIV and the recipientdecryption key RDEC; wherein the recipient encryption key RENC isgenerated using identity information of at least one of the recipient'sancestors; wherein the recipient decryption key RDEC is generated by oneof the authorizers such that the recipient decryption key RDEC isrelated to the recipient encryption key RENC, a root key generationsecret and an associated root key generation parameter, wherein the rootkey generation parameter is generated based on the root key generationsecret, and the root key generation secret is a secret of the rootauthorizer; wherein the recipient encryption key RENC is generated frominformation comprising the identity of the recipient, the recipientpublic key RPUB, and a parameter defining a validity period for therecipient decryption key RDEC.
 85. The method of claim 84, wherein therecipient decryption key RDEC is generated according to a schedule knownto the sender.
 86. non-transitory computer-readable medium comprising acomputer-readable program operable to cause a computer to perform themethod of claim
 85. RDEC.
 87. A system configured to perform the methodof claim 85, the system comprising: at least one computer systemcomprising one or more processors and memory, for acting as saidauthorizer; at least one computer system comprising one or moreprocessors and memory, for acting as said sender; and a plurality ofcomputer systems each comprising one or more processors and memory,acting as said authorizers.
 88. The method of claim 84, wherein therecipient private key RPRIV and the recipient public key RPUB aregenerated using system parameters issued by one or more of theauthorizers.
 89. The method of claim 84, wherein the recipientdecryption key RDEC is related to the root key generation secret and theassociated root key generation parameter.
 90. The method of claim 84,wherein the plurality of authorizers further includes at least mlower-level authorizers in the hierarchy between the root authorizer andthe sender, wherein m≧1, and wherein l of the in authorizers in thehierarchy are common ancestors to both the sender and the recipient,wherein authorizer_(l) is the lowest common ancestor authorizer betweenthe sender and the recipient, and wherein l≧1, and wherein: alower-level key generation secret is selected for each of the mlower-level authorizers in the hierarchy between the root authorizer andthe sender; and a sender decryption key SDEC is generated such that thesender decryption key SDEC is related to at least the root keygeneration secret and one or more of the m lower-level key generationsecrets associated with the m lower-level authorizers in the hierarchybetween the root authorizer and the sender; wherein the message isencrypted using at least the sender decryption key SDEC and one or moreof the lower-level key generation parameters associated with the (m−l+1)authorizers between the root authorizer and the sender that are at orbelow the level of the lowest common ancestor authorizer_(l), but notusing any of the lower-level key generation parameters that areassociated with the (l−1) authorizers above the lowest common ancestorauthorizer_(l); and wherein the encrypted digital message is decryptableusing at least the recipient decryption key RDEC and one or more of thelower-level key generation parameters associated with the (n−l+1)authorizers between the root authorizer and the sender that are at orbelow the level of the lowest common ancestor authorizer_(l), but notusing any of the lower-level key generation parameters that areassociated with the (l−1) authorizers that above the lowest commonancestor authorizer_(l).
 91. A non-transitory computer-readable mediumcomprising a computer-readable program operable to cause a computer toperform the method of claim
 90. 92. The method of claim 84 furthercomprising generating, by at least one machine in the set of the one ormore machines, the recipient decryption key RDEC by one of theauthorizers.
 93. A non-transitory computer-readable medium comprising acomputer-readable computer program operable to cause a computer toperform the method of claim
 84. 94. A method for operating a public-keyencryption scheme which provides for sending a digital message between asender and a recipient with participation of a plurality of authorizers,the plurality of authorizers including a root authorizer and nlower-level authorizers in a hierarchy between the root authorizer andthe recipient, wherein n≧1, wherein the digital message is encrypted bythe sender using a recipient public key RPUB and a recipient encryptionkey RENC to create an encrypted digital message for decryption by therecipient using a recipient private key RPRIV and a recipient decryptionkey RDEC, the method comprising one of the authorizers generating, by atleast one machine in a set of one or more machines, the recipientdecryption key RDEC such that the recipient decryption key RDEC isrelated to the recipient encryption key RENC, a root key generationsecret and an associated root key generation parameter, wherein the rootkey generation parameter is generated based on the root key generationsecret, and the root key generation secret is a secret of the rootauthorizer; wherein the recipient encryption key RENC is generated usingidentity information of at least one of the recipient's ancestors;wherein the recipient encryption key RENC and the recipient decryptionkey RDEC are a public key/private key pair 1; wherein the recipientpublic key RPUB and the recipient private key RPRIV are a publickey/private key pair 2, wherein the recipient private key RPRIV is asecret of the recipient; wherein the recipient encryption key RENC isgenerated from information comprising the identity of the recipient, therecipient public key RPUB, and a parameter defining a validity periodfor the recipient decryption key RDEC.
 95. The method of claim 94,wherein the recipient decryption key RDEC is generated according to aschedule known to the sender.
 96. The method of claim 94, wherein therecipient private key RPRIV and the recipient public key RPUB aregenerated using system parameters issued by one or more of theauthorizers.
 97. The method of claim 94, wherein the recipientdecryption key RDEC is related to the root key generation secret and theassociated root key generation parameter.
 98. The method of claim 94,wherein the plurality of authorizers further includes at least mlower-level authorizers in the hierarchy between the root authorizer andthe sender, wherein m≧1, and wherein l of the m authorizers in thehierarchy are common ancestors to both the sender and the recipient,wherein authorizer_(l) is the lowest common ancestor authorizer betweenthe sender and the recipient, and wherein l≧1, and wherein: alower-level key generation secret is selected for each of the mlower-level authorizers in the hierarchy between the root authorizer andthe sender; and a sender decryption key SDEC is generated such that thesender decryption key SDEC is related to at least the root keygeneration secret and one or more of the m lower-level key generationsecrets associated with the m lower-level authorizers in the hierarchybetween the root authorizer and the sender; wherein the message isencrypted using at least the sender decryption key SDEC and one or moreof the lower-level key generation parameters associated with the (m−l+1)authorizers between the root authorizer and the sender that are at orbelow the level of the lowest common ancestor authorizer_(l), but notusing any of the lower-level key generation parameters that areassociated with the (l−1) authorizers above the lowest common ancestorauthorize_(l), and wherein the encrypted digital message is decryptableusing at least the recipient decryption key RDEC and one or more of thelower-level key generation parameters associated with the (n−l+1)authorizers between the root authorizer and the sender that are at orbelow the level of the lowest common ancestor authorizer_(l), but notusing any of the lower-level key generation parameters that areassociated with the (l−1) authorizers that above the lowest commonancestor authorizer_(l).
 99. A non-transitory computer-readable mediumcomprising a computer-readable computer program operable to cause acomputer to perform the method of claim 94.